BAS, the union carpenter is also getting benefits (medical, retirement, etc). I would imagine a "handyman" that works for a company (more of a "maintenance" man) probably makes $15-20/hour.
These "handyman" companies are guys that are self-employed. I wouldn't hire a handyman to come into my house for $20/hour because he probably doesn't know what the fuck he's doing!
First of all, what they charge varies by region (in Florida I paid $45 to have a 2000sq ft 4br house cleaned, here in DC I pay $75 for a 1200sqft 3br).
These guys have to have a business license, insurance, etc. They also have overhead (their vehicle, gas, insurance, supplies, tools, etc). There's no way some dude is going to drive to your house and do a 1 hour job for $20...then drive 15 miles to his next job for $20....and so forth.
Hell, there's a place less than a mile from my house where all the illegal's hang out for "day work". They usually ask for AT LEAST $10/hour. You have to bargain with them. But they usually start around $15 and will not go below $10 (from my experience, and my neighbors who have hired them for odd yard work type jobs).
Additionally, most of them will ask you what you want done....and they usually will quote you a price for the job. Similar to what flooring guys do (they'll generally charge you per square foot....sometimes it may take 4 hours to do the job...and sometimes it may take 6 to do the same amount of square footage).
They "make" around $50/hour...but they probably only charge 4-6 hours/day unless they have an all-day job. So, they are making $200-$400/day.