Modern Palma is NOT based on 7.62X51mm NATO and back in the days when the host country for the Palma international team matches provided competitors with both rifles and ammunition, the USA provided specially built Winchester M70 'Ultramatch' .308 Win calibre target rifles as long ago as 1976.
http://riflemansjournal.blogspot.co.uk/2010/08/history-history-of-palma-match.html
... and 25,000 rounds of .308W ammo was loaded for that year's competition by Winchester-Western using 190gn match bullets. This applied to all subsequent US hosted 'Palma' rounds while these arrangements applied.
However, in that era, when hosted by GB or British Commonwealth countries, 7.62mm TR ('Target Rifle') rifles were supplied and standard 7.62mm NATO ball ammo issued to all competitors, because that is what these countries used in their domestic matches.
Target / Fullbore rifle evolved out of various western nations' old 'Service Rifle' disciplines that used the local service rifle and cartridge. That is derivations of the M1896 Mauser in Sweden and the milspec version of 6.5X55mm, the Enfield Number 4 rifle and Pattern '14 in GB and the British Commonwealth with the .303 Mk 7 ball round and so on and so forth. These were slowfire matches shot over every distance from 200 to 1,000 yards with the exception of 700 yards for some reason.
There was either little or even no direct US equivalent as High-Power Service Rifle in the USA was always a different discipline which involved various shooting positions, rapid-fire, and in-stage compulsory reloads. However, I'm sure that M1 Garands and M1903 Springfields were also employed in various multi distance slowfire matches out to 1,000 yards as was the case in Scandinavia and the British Commonwealth, but it wasn't the primary discipline. Even though magazine rifles were employed, the GB / European model specifically banned the use of the magazine other than as a loading platform, and single-loading was compulsory.
When these countries adopted the 7.62mm as their military cartridge during the 1950s, this caused them great difficulty in the formal prone target shooting activity rules. Many of the older military rifles proved unsuitable or only marginally suitable for the higher pressure 7.62mm, but the tradition was to use the current military cartridge and all were keen to carry on with this. (There were financial advantages too back in the 60s/70s as most governments and defence departments provided free or heavily subsidised milspec cartridges to their shooting national governing bodies.) Eventually, the 'Target Rifle' discipline was adopted using heavy barrel single shot rifles, this taking place in the UK over 1967/68, rifles chambered for the standard NATO ball round, which was specified with a 144 to 147gn FMJBT bullet at a nominal 2,800 fps. A great deal of development work had to be done to adapt the No.4 rifle to the 7.62mm, the main changes being the substitution of a barrel that was very much longer (25" increased to 30") and of a VERY much heavier profile. The military rifle woodwork and bedding didn't suit this barrel, so there was a forced move to a chopped off forend and handguard and the barrel was free-floated with some action bedding changes. The 7.62 was found to have relatively poor accuracy and inadequate long-range performance, so various other measures were adopted to ameliorate these issues, primarily very tight bore barrels to get MVs up and a 1-14" rifling twist rate to reduce the spin rate on these bullets with poor concentricity.
While there was no doubt a great deal of discussion within the US shooting bodies over the NATO led changes, there was no equivalent redrawing of the primary discipline as in the UK. The M14 and 7.62X51mm joined the M1903 and M1 in .30-06 as eligible combinations, I imagine the M1 in 7.62mm form too as the US Navy adopted this modification instead of the M14 ... and another generation later, the AR15/M16 in 5.56/.223 joined the procession.
At some point or other, the US based International Palma committee changed the rules for the ammunition to be used in the three yearly international events to make the 155gn HPBT match bullet compulsory, that is the original Sierra Palma MatchKing p/n 2155. Later, the rules for both Palma and Fullbore Rifle (which encompasses 'Target Rifle') changed the rules to insist on use of a bullet that weighs 'less than 156gn'. The various national bodies which regulate their local versions of Palma Rifle / Fullbore Rifle / Target Rifle formed a body called ICFRA (the International Confederation of Fullbore Rifle Associations) to set international regulations and standards on overall weights, minimum trigger pull weight, cartridge specs, target dimensions, how matches are run, courses of fire etc. At a yet later date, .223 was added to .308. For many years, all ICFRA regulations, papers etc routinely referred to the two cartridges under their twin civilian and military designations, even though there are differences in their specifications. ie 5.56mm/.223 Rem and 7.62mm/.308 Win. That went back to the historic and national differences in practices referred to. Some years ago, ICFRA removed EVERY reference to 5.56mm and 7.62mm from all documents and regulations. This was because (1) all modern TR / FB / Palma Rifle chambers and barrels are for .223 and .308, also because 5.56mm and 7.62mm are now legally defined as 'military' and there are restrictions in many parts of the world on their civilian use, also affecting such weapons and ammunition being carried on international transport and crossing international borders. For instance, IATA the international airline operators trade body, has agreed with the UN Inter-Governmental Commission on Reducing the Supply of Smallarms that none of its members will carry any miliatry calibre weapon or ammunition on civil flights.
So, what are the differences between the Savage F/TR and Palma models? Does the Palma have a 7.62mm chamber? I don't know what Savage uses, but when Stumpy1 says the factory uses a reamer made to the Palma 95 specification that sounds correct. I have in front of me, PT&G's 'The Gunsmithing Book of Chamber Prints' and what headspace does it give for the .308 Palma 95? It is drawn as 'minimum 1.630"' for the Palma 95, likewise that of the .308 Palma Bisely 150 Rule which is that used by many British gunsmiths in building TR rifles, likewise that of SAAMI .308 Win, .308 Obermeyer Match ... I could go on.
When these rifles are imported into Europe and the UK, it is a legal requirement that they undergo proof testing before sale. Either model of Savage 12 Competition rifle is 'proofed' as .308 Winchester and stamped as such in the UK's London or Birmingham proof house. 7.62X51mm NATO cal. rifles use a different specification proof cartridge and are stamped up differently on acceptance.
The GO gauge for .308 Win is 1.630" too while that for 7.62 NATO is 1.635", and every other dimension is larger by a significant amount. These rifles are NOT chambered for 7.62X51mm NATO. Moreover, the ammuntion used in every country that has these (Palma / TR) rifles of any make and model says .308 Winchester on the carton. The UK ammunition supplied by the GB NRA is .308 Win RWS ammunition specially made to suit a slightly tight barrel .308 Win rifle with a 30-inch barrel to produce around 2,925 fps from the original Sierra 155 (#2155). it says .308 Win on the box and the case dimensions are specified for that cartridge and chamber as laid down by the US SAAMI organisation.
So, what are the differences between the two .308 WIN Savage Model 12 competition rifles? The chamber up to the case-mouth is likely identical. The throat on the Palma model will be that of the Palma 95 chamber or similar with freebore designed to suit the short 155gn Sierra (#2155) and similar designs. Ahead of there, the rifling pitch is one turn in 13 inches adopted some years back alongside the original 155gn SMK, although many TR / FB / Palma competitors now specify 1-12" on custom rifles as today's 155s have become longer and the 13-inch twist rate has become marginal in the views of some.
The 12 F/TR rifle is different in at least one respect - it has a one in 12 inches twist rate as F/TR does not limit bullet weight in most countries, certainly not in the US or UK (but yes in Canada and some others). To make any sense of the 12" twist, it likely has been given a bit more freebore to handle longer, heavier bullets seated to beyond 2.800" COAL. The 12-inch rate is ideal for the 185gn Berger LRBT 'Juggernaut', but a Palma 95 freebore is overly restrictive forcing handloaders to seat the bullet too deep in the case.