Branch Number, Transit Number, Institution Number, Account Number: What are all these things?

I encountered the following fields on a government form required to set up electronic payments and I couldn’t figure out what each meant:

This seems to happen every time I am asked for this information; to avoid having to phone the credit union every time, I’m documenting this here.

• Branch Number (also known as Transit Number) – According to Wikipedia, “Each branch in a financial institution is assigned a unique transit number for identification. The final digit of the transit number indicates the geographical location of the branch.” At Provincial Credit Union, the number is 39073.
• Institution Number (also known as Bank Code, Financial Institution Number) – Each bank and credit union has one. Provincial Credit Union’s number is 839.
• Bank Account Number – what it seems, just my regular old bank account number.