I assume you are asking about other people flying in VATSIM so the answer is a definite yes.

Sure. Actually in order to connect to VATSIM you need an application to establish communication between your FS and the VATSIM server you are connected to. Such applications are Squawkbox and FSInn and it is this application which handles the way you see other people, not the FS itself.

Even people using different connecting applicaitons (Squawkbox and FSInn) or different versions to see each other.

However you must remember that what you see is how your connector application, for example SB3 (squawkbox v3) translates the other aircraft. A very special aircraft may not be known to SB3 (or FSInn) in which case the other aircraft is displayed identical to yours. So, it may be possible to see a custom air glider as a 737 if you fly a 737.

The same issue may occur for liveries, if the other person uses an aircraft in a fictious and unknown livery.

I use SB3. Never used FSINN. However I know FSINN has an additional feature.

When you fly with SB3 your aircrafts data (position, speed) are communicated between you and the other players via the SB server no matter if you fly next to each other or on the opposite sides of the earth.

With FSINN the above functionality is identical except when you are very close to the other aircraft. When this happens a peer-to-peer connection is established between your PC and the other pilot's PC. This way the position and speed updating is much faster and you can easier fly in formation. As far as I know you can disable the peer-to-peer feature if you don't want to allow direct access to your PC.