There were 'officially' two main versions of the handlink throughout the series: the "calculator" handlink and "gummi bear" handlink, as you mentioned.
However, there were different versions of each of these throughout the series, both because of Don Bellisario's request for an unrecognizable handlink and because it's been said Dean Stockwell frequently broke the handlink props during filming.
The first version of the handlink is in "Genesis" and is basically a thin, clear, acrylic, pad with no lights or electronics at all, making version 1.0.
Throughout the rest of Season 1, more and more L.E.D.s and electronics were added to this, making version 1.1.
Season 2 had a larger budget since the show was officially picked up for a full season, and the 'complete' version 1.2 became the "calculator" version.
Season 3 had some episodes whose air dates were out of sequence with the order in which the episodes were actually filmed, so in "The Boogiem@n," (version 2.1) the gummi handlink first appeared despite the fact that it doesn't get officially introduced until "The Great Spontini." The gummi handlink in "The Great Spontini" has a slightly more crude look to it, as it was probably still being perfected at the time, creating version 2.0. As mentioned earlier, these episodes were aired out of filiming sequence, so the final version appeared before the more crude version.
("The Great Spontini" screenshot not available.)
Finally, one last version with barely noticeable differences can be seen in other episodes, namely "Lee Harvey Oswald" (version 2.2), with only some colored cubes' edges slightly different from the most used version.
