To play TBC, do I need to make a new account for that client? Or use this one?

So I have the Wotlk client and an account (clearly) but, once I download the TBC client, can I use this account for that client to play on those servers?

Also, is there anyway to get both expansions on the same client at all or do they have to be separate?

Thanks in advance!

same login for all expansions. each expansion requires it's own client to play.

Thanks a lot!

You can log into every expansion with the same account. You just have to have the appropriate client versions and you're good to go.