It's not just the width of the bottom bracket shell that determines the bottom bracket type. If yours is engraved "36x24TPI" it is ITALIAN, period. Italian bb's are the only ones with 36 mm diameter cups and 24 tpi thread pitch. Nothing else is the same.

All Italian bottom brackets are right hand threaded on both cups. To keep them form spontaneously loosenening, Italian drive side cuts are torqued VERY tight so that may be why yours is hard to break loose.