If I have multiple HTML tags with separate submit forms, how do I know which when was posted in the PHP file that processes the form's data?
The easiest way is to name your submit buttons unique to the form. You can also use this if you have multiple submit buttons for a SINGLE form (eg - submit and save, submit and return, submit and exit)
<input type=submit name=action value=Save>
<input type=submit name=action value=Return>
<input type=submit name=action value=Exit>
The $_POST array (or $_GET/$_REQUEST) will contain the key action with the value of the enacted button (whether clicked or not).
As a rule, I avoid passing hidden text fields, etc, that are unnecessary - simply to keep the code more clean.
So. For your application, I'd give your submit button values as such:
<form id=Form1>
<input type=submit name=action value=Form1>
</form>
<form id=Form2>
<input type=submit name=action value=Form2>
</form>
<form id=Form3>
<input type=submit name=action value=Form3>
</form>
