'Tabby' refers to a cat with a striped coat (examples here: http://www.catster.com/cats-101/tabby-cat), and has nothing to do with a cat's sex. Tabbies can be male or female. Female cats are sometimes called 'molly cats' or 'mollies' but those terms are not very common outside cat fanciers. However, 'tomcat' or 'tom' (for a male cat) is more widely used.
Kitten is "un chaton". Specifically a female kitten might be called a "minette" (minou for male cat) or "petite chatte" (these might be slang terms...wait for Remy or Sitesurf's approval), but as far as I know, all kittens are called chaton regardless of gender.
How does "C'est un chat" differ from "C'est une chatte" in the sound? Could I even hear the difference? If there is no difference detectable, shouldn't both solutions be correct here?
Chatte = Sounds like someone saying "shh!" and "hat" stuck together. Or, William Shatner's nickname "the ❤❤❤❤".
Chat = Sounds like someone saying "shh!" and "uh" stuck together. "uh" as is when you're struggling to find a word sort of sound.
In sound this is 'This is a cat', but the translation is 'This is a female cat'. Confusing right?
New to this app....so stoked to see so many others interested in the French language! But in this discussion I believe it is simply a gender difference with un "chat" et une "chatte" unless there is a cultural significance with the difference that I am un-aware of..