You can do transfers from bank account to bank account, or from postal account to postal account, or mix-n-match the two.
I presume you're asking this in relation to your online shopping? Those transactions are commonly handled by bank transfer, by remittance through a bank or post office using a payment slip they send you, by C.O.D., or by credit/debit card payment. That's for domestic stuff, of course. A great many Japanese online merchants seem to not be set up for credit card sales and to not be set up to handle overseas sales.
There are a few services akin to PayPal, but I have never used them and can't give you any specific information on them.