According to Collins ...
A wire transfer is a direct payment of money from one bank account into another
Bank transfer ... a payment between two bank accounts
So, both wire transfer and bank transfer are defined as a transfer of money from one bank account to another. Although "wire transfer" may originally have referred to a particular form of bank transfer it remains widely used regardless of the actual means of transfer. They are both forms of money transfer executed by a bank or by an agent interacting with a bank on your behalf. So, if the context is money transferred between two bank accounts then I think you can use either "wire transfer" or "bank transfer".
The phrase "money transfer" is more general, if one party removes some cash from his/her wallet and hands it to another party then a money transfer has taken place but it is not a "bank transfer" or "wire transfer". That said, context might be enough to make clear that the type of "money transfer" in question is a formal or bank intermediated one
but if it is important to indicate the specific nature of a money transfer then using "bank transfer" or "wire transfer" might be more appropriate.
A remittance is a sum of money that you send to someone.
Remittance describes the money which is being transferred
An appropriation is an amount of money that a government or organization reserves for a particular purpose.
I don't think this belongs with the other terms, although an appropriation is (eventually) money it is not necessarily "bank" or "wire" transferred.