How does the garbage man pick up the smaller trash can?

I don’t know how they do it in San Diego, here they use a cable attached to a winch on the smaller cans that don’t fit their equipment, unless they are light enough to lift by hand.

The lifter, on the trash trucks in my city, are capable of picking up of both. The adjustments are made by the driver, on the dashboard of his truck. This is the trash truck that picks up recycled material, not the truck that picks up everything else.

In LA the cans are all the same size and the trucks for trash and recycling have lifts on the front that pick ‘em up and shake them over the bin in back.

In NYC, residential trash in bags is piled in stinking heaps on the sidewalk where “NY’s strongest” pick them up by hand and toss them into the gaping maw of the waiting truck.

Commercial buildings and businesses have to hire a private hauler and there are all sorts of ways they handle the trash. There are pre-compacted-and-baled blocks of trash loaded by automated gadgets and haulers who have magnificent landscapes painted on the sides of trucks clean enough to eat off and scavengers in wrecks looking for anything of possible value to snatch before the official collector gets there.
There’s lots of varieties of solutions depending on whether there is a municipal system or private haulers or some mix.

How about you wait by the window on trash day, watch how they do that where you live and report back?

Yes, I agree with @ dabbler, and why not watch to see for yourself? ;-)
Trash pickup is an adventure here where I live in a rural Sierra Nevada foothill community.
I live on a small private road with only 3 homes each on 10 acre parcels. My neighbors complained that the trash truck is tearing up our tiny road so now everyone hauls their cans to the end of the road. Major pain in the ass, but hey, I told my neighbor if he was that concerned he can pick up my can in his truck too because there is no way I am wrestling my trash can into the trunk of my car.

We also contend with one neighborhood dog that likes to dump the cans, mine has a locking lid but I have to laugh when I see old ranch Rover doing his thing, tipping over peoples cans at the ends of their roads, driveways. Our trash guys also are very lax about letting our cans roll away, lids in the weeds, cans somewhere down the hill. Country trash guys are pretty laid back up here. lol

Yes it falls under the category of the recycling truck. The man manually came down and he picked the excess can by hand.

Our trucks have arms that open up and then close around the can like a big hug, no matter what size it is. The garbage man rarely ever gets out of the truck.