When I was building my Rodd.com kit I studied the movie as well as I could at the time and thought I saw at least three different tricorders. Going over it again I can spot four different ones in the film.
The first is unique in that it has the folding upper panel and very different sensors. It is seen in the early parts of the movie and is the one that Decker hands to Spock on the bridge, and Scotty is using in engineering.
The next one we see is is held by Spock on the bridge when they are being scanned by V'ger. I can only tell that this one is not the first one for certain, but the sensors look like the one Spock uses at the films climax.
The next one is held by Ilia in the same scene. This one can be identified by the two dark rectangles on the sides where they join the top.
When Ilia is digitized and drops her tricorder, it's yet another one that has different control graphics that are wider spaced and no black rectangles.
Then Kirk picks it up and it's the black rectangle one again.
Now we move on to the movie climax and Spock is holding the one he held during the V'ger scan scene but we get a nice good look at the sensor array.
And Decker is holding another. No black rectangles and the sensors like the one I made and more like the Rodd.com kit's look. It also looks to have a plate on the bottom.
So how many different ones is that? I come up with four variants.