Yes you can:

in javascript:
<input type "button" onclick "add();" name "sub" value "add" />
<input type "button" onclick "edit();" name "sub" value "edit" />

and use
document.getElementById("formname").action "something.php";
document.getElementById("formname").submit();

or with PHP:
<input type "submit" name "sub" value "add"> <input type "submit" name "sub" value "edit">

you will have $_POST['sub'] equals "add" or "edit"
you can then use if or switch as you see fit in your server script.