I noticed that address that Start with b use fewer transaction fee than one that starts with 1, or there is more to this transaction of a thing that I still need to learn more about?
Segwit address start with bc1, not just b.
This threads can also help you:
Minimizing bitcoin transaction fee Pay-to-taproot (P2TR) transaction feeAnd the address starting with b might be right if they are Segwit addresses, as in bc1..., they could save you about 16% of the fee. But you have to consider the Mempool while doing the transaction too.
If 1 input and 2 outputs of legacy to legacy transaction is compared with segwit to segwit, there should be 42% fee reduction.
Transaction fees depend on transaction size which again depends on inputs and outputs.
It is virtual size (vsize or vbyte), or transaction weight that is considered. But if it is legacy address transaction, the size is the same as the virtual size, but not for nested and native segwit.