I think it probably depends on country, here in UK commuter is usually more than 2 coaches long, usually electric (overhead or third rail)
This is a commuter train that I normally see. But as with most things there are some exceptions, I have seen 2 coach commuter trains and there are diesel commuter trains on some unelectrified lines.
Regional trains here are usually 2 coaches and mostly diesel
There are probably some exceptions but i'd be surprised if there were electric regional trains as electrification is fairly poor in this country. Anyway for me that is generally the difference between commuter and regional trains, i'd be interested to see what its like in other countries

This is a commuter train that I normally see. But as with most things there are some exceptions, I have seen 2 coach commuter trains and there are diesel commuter trains on some unelectrified lines.
Regional trains here are usually 2 coaches and mostly diesel

There are probably some exceptions but i'd be surprised if there were electric regional trains as electrification is fairly poor in this country. Anyway for me that is generally the difference between commuter and regional trains, i'd be interested to see what its like in other countries