Commuting is getting you from your home to your first work location... and then from your last work location back home.
If you, therefore, (a) drive from home to employer, (b) from employer to business, (c) from business to employer, and then (d) from employer back home, only (a) and (d) represent commuting... (b) and (c) count as travel.
I kind of hesitate to say this, because some people will overreact to this and go ape... but I may as well say it... You can work the commuting rules to get more business miles sometimes. E.g., what if in your business, your first work location is your home office and your last work location is your home office.
By the way, I don't mean this "wink-wink, nudge-nudge"... I mean you really, really do run your business this way. In this special situation, your commuting and business miles maybe look like this...
You grab a cup of hot french roast in the kitchen and (a) commute from the kitchen to your home office, then (b) from your home office to client, then (c) from your client back from your home office, and finally (d) from your home office to the kitchen where you grab a IPA from the fridge.
In this case, I think (a) and (d) count as your commutes and (b) and (c) count as travel.