There are only very minor differences.
The ConneCTion was originally developed for the North American market and the shell had the words "Tamagotchi Connection" screen printed on the front.
The ConneXion was (more or less) developed for the European/Asian/Australasian market and the shell only had the words "Tamagotchi" screen printed on the front.
Small differences in wording were noticeable between the ConneCTion and the ConneXion - for example, Time Out versus Punish, Away versus Absent (there are several others);
there were also small differences in animations such as a Snake/Jack in the Box as one of the bad presents on the ConneCTion versus a Ghost on the ConneXion.
Other than these types of differences, there is not much between the two types of Tamagotchi. The differences are most noticable in the V1s, there were fewer in the V2 (Time Out is used instead of Punish on the ConneXions for example) - although some of the items names were slightly different and I haven't taken the time to note any differences on the V3...
That's about it really. This list is not exhaustive.
Like I said, there are several other differences I could have given you - but none of them really affect play with the Tamas, they are just one of those interesting things to note.
I am sure that if I have forgotten any really big differences one of the TamaTalkers will jump right in and tell you (and me)