Gravity forms customize field markup for the same form appearing in different places

You have three ways:

1) To find out the correct hook (at this moment i can tell if it even exists for that)

2) To use only CSS (For example, just target your first form with #header .form-group{} ( or by its another parent div, instead of #header )

3) Use the GLOBAL variable to count each time whenever that function executes. i.e, see example:

add_filter( ........... );
function ..........{
    $GLOBALS['my_form_counter'] = empty($GLOBALS['my_form_counter']) ? 1 : $GLOBALS['my_form_counter'] + 1;
    if($GLOBALS['my_form_counter'] == 1){
       //it's the first time of the form EXECUTION, so you know where it is happening.. Code what you want
    }

    if($GLOBALS['my_form_counter'] == 2){
       //it's the second time of the form EXECUTION, so do now what you want
    }
}