In terms of the official International Confederation of Fullbore Rifle Associations (ICFRA) rules, there are two classes:
F-TR: 223 or 308 (or military equivalents) any bullet weight, any sight, and must not exceed 8.25 kg including all attachments. Bipod or sling only, no front pedestal rests.
F-Open: Any caliber up to 8mm, any sight, any front rest, and must not weigh more than 10 kg.
Some provincial rifle associations (BC, AB, ON that I know of) and clubs have factory classes that have specific definitions, and as such, the factory rifles may be classified differently, but in a true F-Class match, these are the two classes.
Here are the rules chapter and verse...
F2. TECHNICAL SPECIFICATION of RIFLES and AMMUNITION
F2.1. Two separate rifle classes are recognized under F-Class rules, Open and Restricted. The differences are in the calibres, rifle maximum weight and rests allowed.
F2.2. An ‘F’ Class Open rifle may be of any calibre up to and including 8mm and the overall weight must not exceed 10kg including all attachments (such as, but not limited to, its sights and bipod, if any). NB: An ‘attachment’ is defined as including any external object (other than the competitor, his sling (if any) and his apparel) which recoils (or partially recoils)
with the rifle, or which is clamped, magnetically or viscously held, or in any other way
joined to the rifle for each shot, or which even slightly rises with the rifle when vertically
lifting the latter from its rest(s).
F2.3. An ‘F’ Class Restricted rifle is limited to .223 Remington or .308 Winchester calibre
chambers or their commercial metrification equivalents. Chamber dimensions must conform
to SAAMI or CIP dimensions. Ammunition may be commercially made or hand-loaded as
defined in Rule F2.23. There is no restriction on bullet weight. The Restricted rifle class is
limited to the use of an attached bipod and/or a sling as front supports, optionally together
with a rear bag which provides no positive mechanical means of returning the rifle to its
precise point of aim for the next shot . The overall weight must not exceed 8.25kg including
all attachments (such as, but not limited to, its sights and bipod, if any). NB: An ‘attachment’
is defined as in Rule F2.2. All other Technical Rules apply.