computer architecture – Transistors collector input output of other transistor?

I’m new to computer science and trying to learn the basics. Have learnt how to create logical gates using simple components like relays, thanks to nandgame.com. This was easy, boolean functions, have no problem with that. Now I have a very basic question about transistors.

Normally, in computer processors, is the collector of a transistor an always-on current, like, a 1 in binary, and the output regulated by the base/gate only, or do they tend to be connected in series, with collector taking a binary input that is either 1 or 0?

enter image description here

I got the impression somehow that the collector does not tend to take a binary input. At the same time, with the relays on nandgame.com, it is very convenient to use their “collector” for binary input, this lets a single relay be an AND gate, etc. So, maybe someone understands what I’m asking and why and can point me in the right direction.