the keys are 33 bytes for standard ECDSA public keys and 32 bytes for BIP340 compliant pubkeys, they have the extra bit (it's an extra byte just for 1 bit) as it uses a funny scheme which essentially shaves one bit of security for a much neater format, the way it works is that if it comes out odd (the first, least significant bit) then it inverts (bitwise NOT) and then it can omit that bit and it's a neat 32 bytes, or equal to 4x64 bit words

the schnorr signatures are 64 bytes long, and ecdsa signatures can be anywhere between 62 and 67, iirc, but they are not a consistent length unlike Schnorr, and usually they are 65 bytes, but not always

the reason for the change is that computing it and splicing together protocol messages is easier if you don't have to overflow into another 8 bit word... iirc, the actual modular arithmetic done for schnorr signatures and public keys is done on 4x64bit words, you can see this if you follow the computations into the back end, inside the key is a pair of ModNScalar i forget exactly, i haven't honestly gone that deep into it except to know that you can do some neat things other than just signatures and pubkeys with them, like the scheme bitcoin uses that recovers the key instead of checking a key matches a signature - this was done to save space - and it tests the same because you compare your pubkey with the key it generates, it generates a key either way but it has to match the one you want - but never mind that, that's ancient, NIST/NSA ECDSA bullcrap because they were too cheap to buy out schnorr for his far more efficient algorithm patent