The original Tamagotchi release was simple, with just 11 unique characters, there was a second version released soon after that was basically a re-skin. These two versions are called P1 and P2.

After that some "spinoffs" released.

The next major entry was Tamagotchi Mesutchi & Osutchi, which had two gimmicks, the first one is that each shell could include either female or male characters, and the second one is that breeding them could give you tamagotchis of higher tiers if you took care of them well enough.
The map starts getting complicated but I included female and male versions in the same square and sorted them from higher to lower tier from left to right. (You would always start with the baby on the far right).

A new generation of Tamagotchi gets released called Tamagotchi Connection. This is Tamagotchi Connection v.1, it introduces a system where odd and even generations would be different, for example: the first time raising a tamagotchi it would always evolve into one from the odd branch, but after breeding, it would result in a tamagotchi that evolves into a character from the even branch, etc...

"Keitai Kaitsuu Tamagotchi Plus" was something pretty similar to the one before, even though it wasn't marketed as Tamagotchi Connection but Tamagotchi Plus.

You could say that Tamagotchi Connection v.2 is just like the previous two releases, but bigger. It also kinda brings back characters from the two (well, it brings back character from the classic releases as well.

Tamagotchi Connection v.3 looks like it's a reskin of its predecessor, with the same ammount of characters and growth system.

"Chou Jinsei Enjoi Tamagotchi Plus" was technically released before Tamagotchi Connection v.3, but I thouhgt it made more sense to list it after. This version introduces a concept of groups or families, most notably 3 which are usually refered to as "smart", "creative" and "easy-going".

Next, Tamagotchi Connection v.4 took the idea planted by Chou Jinsei Enjoi, but you could get any character from the egg and depending on how you raise them they would grow into one of the groups, it also has a "neutral" group that you're more likely to get if you make mistakes raising it. The chart really gets very tangled here because each character has it's own conditions to evolve into different characters.

Tamagotchi Connection v.5 really takes the idea of families and runs with it. You're back to getting three possible babies that only evolve into a limited group of characters. Upon getting married they would also evolve, and certain specific marriages would result in a full family like the ones at the bottom. The lines really get very complicated down there because each adult can evolve into either two or three others.