I agree when it's usually mentioned as having a "7" or "7mm," folks these days are referring to 7mm Mag. As a general rule, cartridges that are most commonly referred to by it's "inches" description - .284, .280 Rem, etc, - are hardly ever actually called 7's in conversation, unless sometimes just discussing the bullet component. So, IMO, in this order of using "7" or "7mm" as the moniker,
- 7mm Rem Mag
- 7mm-08
- 7x57 (Mauser)
Hardly ever, as others have mentioned
- .280 Rem
- .284
People will almost always call these last ones (as well as the likes of 7x30 Waters) by their complete names.
As far as a solid, supported round/platform to pursue, I also agree the 7mm Mag is largely a "waste" or is excessive for most hunting purposes. It requires a longer action, often is more expensive (ammo), and its "report" and shove beyond what many consider desirable for what they need.. BUT, it certainly is capable and supported. But, if I want or feel a need for a magnum, something more than an '06, I'll get a .300 Win Mag for a "do all" or for "just elk and above," something in the .338 class. One of my faves is the classic .35 Whelen, a sunbsonic non-magnum beauty that'll do it under 500 as well as any. But, not largely "supported" for the OP's purposes.
SO, for a general purpose round/rifle, I'd focus instead on, by category:
Standard Action
- .30-06
- .270 Win
Short Action
- .308
- 7mm-08
IMO, no need to look elsewhere--again for the OP's criteria.
Looking at the Standard actions, the two listed do it all and can be loaded up or down, and are found on virtually all LGS shelves nationwide, including "backwoods" general store types (carrying any ammo).
.280 can equal or better .270 but, despite better bullet choices (7's again) is not supported nearly as well for non hand/re-loaders. The .270 is the quintessential "deer" (and sheep) round, and with modern ammo choices has made very decent inroads into the elk territory--to the extent that if it's what you have you no longer have to (as a g.p. hunting set up (as if you ever did really have to) think of a second rifle for an elk hunt.
Looking at the Short actions, .308 does it all about as well as the .30-06 except some heavier loads. 7mm-08 is one of the great under-rated rounds, a necked-down .308, it's less in recoil and report, and arguably more accurate under 300. The 7mm-08 to me can make for the quintessential "mountain rifle" as it seems to thrive in all barrel lengths but, unlike some, is particularly tolerant of the shorter barrels (18-20). Both it and the .308 are available most anywhere, but the .308 does reign supreme in that department by a good margin.
Hard to beat a 22" 7mm-08 or .308 as a do-all round.
All others than the four main ones above--of the general purpose bolt, pump or auto platforms--are pretenders IMO in the "well supported" department--rifles and ammo.