Is there a name for this kind of word trick?
Park on the driveway, drive on the parkway.
Send a shipment by road, send a cargo by water
Cottleston, cottleston, cottleston pie, A fly can’t bird, but a bird can fly.
noses run, feet smell
And any more examples of this trick?
The best example I know is a “word palindrome”:
You can cage a swallow, can’t you, but you can’t swallow a cage, can you?
This isn’t really a thread game. I’m going to shift this over to IMHO, since you’re looking for other examples as well.
I think I might call this a form of chiasmus. From the link:
I hear it in things like the Mae West quote “it’s not the men in my life that count, it’s the life in my men”, that sort of thing.
George Carlin had a whole routine about words and which order you say them.
The only part of it I remember was “it’s okay to prick your finger, but not to finger your prick”.
There may also have been some more ,well, subtle, examples,…but I was 13 when I heard him. 
I learned that Cottleston Pie verse as “A fly can’t butter, but butter can fly.”
It makes a bit more sense because bird isn’t a verb, but butter is.
And it makes fun of the fact that the speaker doesn’t quite grasp the concept of a butterfly.
I’d rather have a bottle in front of me than a frontal lobotomy.
I’d rather have a free bottle in front o’ me than a pre-frontal lobotomy.