TMGC+C. November 2008. The first color-screen model.
Exmotchi. November 2008. A TMGC+C based on the Japanese band "Exile". It seems only the shell is different.
Hexagontchi. July 2009. A TMGC+C based on the Japanese TV show "Quiz! Hexagon". Different games, and some different characters. Some Happy/Friendship items are related to correctly answering multiple choice quizes - which are in Japanese, so unless you can read some Japanese, you'll have to resort to randomly guessing.
Tamagotchi-iD. November 2009. Fewer built-in games and fewer built-in travel destinations than the TMGC+C, but new games, foods, toys, etc. can be transferred to it via IR. Happy/Friendship items are no longer the same for every adult character; each type of character has their own set now. Can no longer plant seeds and raise trees. (Successfully raising a tree to maturity would reward the character with money / an item / a food.) These two topics also list some of the differences between the TMGC+C & Tamagotchi-iD:
https://www.tamatalk.com/IB/index.php?showtopic=164579 &
https://www.tamatalk.com/IB/index.php?showtopic=168844 Menu and stats screens translated into English are in this topic:
https://www.tamatalk.com/IB/index.php?showtopic=165502
Tamagotchi-iD Lovely-Melody ver. November 2010. A Tamagotchi-iD with different built-in games, and a few different characters, otherwise very similar to the Tamagotchi-iD original version.
Tamagotchi-iD L. March 2011. Different built-in games, many more characters that can be raised. Can once again use seeds to raise plants that reward the character with an item / a food. Many more built-in travel destinations. (These are unlocked over the generations.) Adult characters can now adopt a pet. Menu and stats screens translated into English are in this topic:
https://www.tamatalk.com/IB/topic/174644-tamagotchi-id-l-menu-stats-screen/
Note: None of the above models have an online TamaTown-type site.