ok so correction, googling base 4 literally returns "Quaternary system" So there's your answer lmao.

just because binary is called binary doesn't mean 10 is binary, 10 is 2 in binary. (Reading from right to left.)

hexadecimal is similar 1F would be 16, assuming i got that correct.

We have the same thing in the decimal system as well. 10 is 10, not decimal, the reason it's referred to as decimal is because it's base 10, meaning that it has deca (10) possibilities it's just used to provide an abstracted method of referring to base systems in word form, without using numbers, because numbers can be a little confusing sometimes.