Both are J-frames and fit the same holsters.
I carried a 637 for years in various pockets and holsters. It carried fairly well in an ankle holster where it got beat up pretty good but I still have.
I bought a 360PD a couple years after they came out and loved it.
I loved it so much I bought a second one to insure I have a spare.
The 360's are a dream to carry. In an ankle holster there is no flopping around. In a belt holster it does not pull my pants askew. In a jacket pocket it does not hang low on one side.
The spare 360, I keep on a length of parachute cord for when I need to run out of the house to attend to something on the property and do not want to suit up. I just hang it around my neck.
I can tolerate 2 cylinders of full-power 357 magnum loads. After that I may as well be throwing the cartridges at the target. So I limit myself to one cylinder of full loads. 38 Specials are cream puffs.
When I want to burn ammo, I have other full-size steel revolvers.
These powerful little revolvers are made to carry not for range work.