The answer to your question is that the difference between the two terms is definitional.   Please let us take a moment to explain that.

The term "I had a bank account" implies ownership.  That is, such a person or entity would "own" the bank account, or hold an ownership interest in that bank account.  In other words, they would treat the account as an asset on a financial statement.

By contrast, the term "I signed on a bank account" does not imply ownership.  Such a bank account is not necessarily an asset belonging to that account signatory, even if that person has the power to move money into and out of the account.  For example, a company comptroller (employee) working for a business may be a "signatory" of that firm's bank account, who can legally make deposits and write checks to pay company bills.  But that is not the same thing as this employee owing the company's foreign bank account, as they cannot consider the bank account as their own personal asset, to do with as they choose.

Does that explanation make sense?  Hopefully it does and that the distinction between the two terms is now made clearer.

Thank you for asking about this.