Nikon DX lenses are marked "DX"... Their FX lenses are either unmarked or marked "FX".

Tokina uses the same designations as Nikon.

Sigma marks their crop sensor lenses "DC" (to help remember that, think "digital crop") and their full frame compatible lenses "DG" (maybe "digital general" purpose?).

Tamron marks their crop sensor lenses "Di II" and their full frame compatible lenses "Di".

Canon marks their APS-C crop sensor lenses "EF-S" and their full frame compatible lenses "EF".

Pentax designated their APS-C crop sensor lenses "DA" and their full frame capable lenses "FA".

Sony appears to mark their APS-C crop sensor lenses "DT" and not use any markings on their full frame lenses.

Olympus no longer makes any full frame lenses, AFAIK. All their "Zuiko Digital" marked lenses are micro Four/Thirds crop-only designs. Older "Zuiko" lenses were all film/full frame (but there are no full frame Oly cameras).

The above designations for crop-only lenses came about and started to be used in approx. the 2002 to 2004 time frame. Older lenses from the "dark ages" of film, without any of the above markings you can pretty much assume are full frame capable. (There were some lenses designed specifically for "half frame" 35mm film in years/decades past... Those won't cover the image area of "full frame". But those are quite rare.)

To further confuse things... there are now "mirrorless" lenses too, from many of these manufacturers. Often these are offered in designs and specifications similar to APS-C, but most of those are not interchangeable due to the much shorter "register" (i.e., distance from the mounting flange to the sensor or film plane of the camera, onto which the lens must focus the image). Sony is an exception, marketing both full frame and APS-C size mirrorless cameras and E-mount lenses for both. Fujifilm is also marketing two different formats of mirrorless now (see below).

Nikon's mirrorless lenses are currently marked "Nikon 1" (as are their mirrorless cameras, though there are rumors this may change in the near future).

Tokina currently only makes one lens, a 20mm in Sony full frame mirrorless "E-mount", designated "FE" (same as Sony).

Sigma marks their mirrorless lenses "DN".

Tamron marks their mirrorless lenses "Di III".

Canon marks theirs "EF-M".

Fujifilm has an extensive line of mirrorless lenses for marked "XF" for cameras using APS-C size sensors.

Fuji has also recently introduced a line of "GF" lenses specifically for their new GFX medium format mirrorless camera.

Pentax only has a few "Q-mount" lenses and doesn't use any specific designation.

Sony "E" lenses are for E-mount mirrorless cameras using APS-C sensors and Sony "FE" are for their full frame mirrorless models.

Olympus only makes m4/3 mirrorless cameras, so there is no special designation besides "Zuiko Digital", as noted above.

When we buy a car we expect to use it for a while and then when parts need ‘upgrading’ we either pay for the repairs or get a new car.
Alternatively we lease the car, upgrade it every couple of years and keep paying a lease charge.
BUT when we want a software package we expect the company to keep investing money to upgrade it and then supply us with the upgrades forever, free of charge. If that company decides that is not a way to keep their shareholders happy and wants to lease the packages with perpetual upgrades, we holler that is not fair and the company is greedy! Using that last thought process I should be able to pay a one time fee to my cable company and then get to use their services forever with no additional charges. I can give many more ludicrous examples however the point should be clear. There ain't no free lunch.

I would appreciate advise on purchasing a pre-owned but excellent condition lens .I shoot in RAW with a Nikon D300s.
My need is to improve the sharpness of my photos , notably those at distance. I'm thinking of a zoom 70-200 mm for that longer distance. I think I need a continuous f/2.8 instead of the typical variable f range that is not so good at the top of the range. I'm also thinking of ED glass but what other key features should be on my list?
Also, should i be buying an FX lens instead of DX so if i decide to upgrade to an FX body I assure best compatibility?? I'm assuming DX will work but not as well on the FX model bodies.
Any other tips on which are good sources of used lenses to assure a safe purchase with pre-owned lens would be appreciated.
Thanks much for guidance
drmjp429