I’m NOT an expert, but thought I’d start a response that others can add to (or correct me on).
I’m going to presume when you refer to a “benchrest” rifle, you are not talking about the most common types used for short range benchrest competition? If you are referring to these, I think they are generally quite different in appearance to F-Class rifles. A primary reason is that benchrest rifles are shot from a rest/bags on a bench, while F-Class is a prone discipline (yes, I know that many F-Class shooters are able to shoot from a bench if/when they are unable to shoot prone due to physical limitations). Another difference is range, in that most benchrest is shot at 100 and 200 yds, while F-Class is typically shot at 600 or 1,000 yds. The longer range typically suggests longer barrels and heavier bullets to maintain speed and deal with wind at longer ranges. Classical benchrest competition (for group) consists of 5 shots for record with the goal of creating the smallest possible impact point deviation between hits on target (smallest group). F-Class, on the other hand often consists of 20 rounds for record plus sighters all shot within 22 minutes (there are various formats/lengths of string, etc.). F-Class shooting creates a lot of heat in the barrel, and often suggests heavier barrels to absorb that heat without loosing precision.
Short range benchrest rifles tend to be much shorter than F-Class rigs. Due to range, benchresters also historically employ short, flat-based bullets designed for short range precision. Short range benchrest rifles have also tended toward small, lightly-recoiling rounds (benchrest cartridges such as 6BR, or 6PPC for group competition, and perhaps 30BR for varmint-for-score matches), as precision is the ultimate goal. The goal of precision has also advised shorter, more rigid barrels for benchrest. Current trends in F-Class are moving toward larger cartridges (like .284WIN, 7PRCW, and even magnums like 300WIN MAG). Yes, 6BR (and its hot-rod varients like BRA, BRX, Dasher) are popular, and may be more precise than their bigger relatives, but as long range wind effects are so fundamental to F-Class, most competitors are leaning toward larger, higher BC bullets. The special category of F-Class called F-T/R is limited to .223Rem or .308Win, but those cartridges tend to be loaded with heavier/longer bullets (than found in tactical applications) to take advantage of higher BCs.
If “benchrest” in your question is actually referring to long-range benchrest, then some of the considerations above don’t apply, and long-range benchrest rifles are visually more like F-Class rigs. The strings of fire in long-range benchrest are still much shorter than F-Class.
I think you can find specifics of rifle design/limitation in various rule books, and pictures on this forum.
OK guys, jump on in...