tl;dr: In-universe, there does not appear to be any significant difference between the various logos; both logos appear on-screen together multiple times, and neither of them seems "more official" than the other. Most likely, one is just a newer logo that hasn't yet fully replaced the old one.
There are definitely several versions of the SHIELD logo in Agents of S.H.I.E.L.D.. The first, which I'm calling the "fancy eagle" logo, strongly resembles the logo from the movies:
This logo only appears in a few episodes -- mostly the pilot, and S01E07, "The Hub". Everything this logo appears on (glass doors, meeting rooms walls, some computer equipment and displays) are found in SHIELD HQ or in The Hub. Thus, it seems likely that this is a previous version of the logo, which is still in use in the better-established locations just out of inertia.
The other, the "stylized" eagle, only appears on the TV show (so far). This is the one we see on most of the SHIELD property, including the uniforms, the office supplies, some of the equipment, and pretty much everything found on "The Bus". Thus, it seems like all of the "newer" stuff uses this logo.
Thus, although the issue is never really mentioned on-screen, I think there are two likely scenarios:
- SHIELD is "transitioning" from the fancy eagly to the more modern one, and just haven't finished yet. Things that have been overhauled or replaced recently have the new logo, and everything else still has the old.
- Or, the fancy eagle is a "more formal" logo, used for the higher profile locations, and the other logo is used for the day-to-day stuff.
On a side note, there's actually a third logo that appears briefly in the pilot episode:
This logo appears behind Ward as he's first boarding The Bus, on the wall of a building in what I assume is the SHIELD airport / launch facility. As far as I've seen, we never see this logo again.
Out of universe, my guess is they put the fancier logo in as a way to link SHIELD in the show to SHIELD in the movies, but the newer logo is the one they really wanted, so most of the sets and props going forward just use that one.