Is it a pun?

I always wanted to make up one of these. I don't know what they're called, but here are a couple of my feeble attempts.

A couple of weeks ago I was way down in Alabama. I was visiting some old friends and one of them gave me a present. It was in a little box, and when I opened it there was a ticket that said, "One free evening rental of the party hearse." What? I said. They explained this was an old car that you could rent for special occasions. Cool. So I went ahead a reserved it for the next night. Well, the next evening came, and it was a disaster. Five of my buddies and me loaded into the car, and we started to tell the driver where to go, but he said he had a couple of stops first. Long story short, it was still a working hearse, so we had to pick up a couple of corpses at two different morgues. We figured he'd drop them off at the funeral home, but he was like, OK, where to? We asked if he'd rather make his deliveries. He said nah, and so we had to ride around all night through Mobile with those bodies. The next day I told my aunt what happened. She said, "Now honey, don't you know you never book a gift hearse in the south?"

OK, another.

When I got to the barracks there was only one rack left. I had my doubts because it was covered with these large red spots, like someone had spilled paint on it, but I didn't have a choice. Well, for some reason, for the next few nights I couldn't help but pee the bed. It's embarrassing, but I kept having these accidents. Each time I'd get up and change the sheet and all, expecting the worst in the morning. The thing was, though, the matress was never dirty. Every morning it was as good as new. I expected to at least turn it over or something, but it was clean. One ol' boy standing there saw me looking at the rack and figured out exactly what I was pondering. "Don't you know boy, a blotched cot never soils?"