In terms of the meaning 'put (a piece of clothing) on', yes, they are the same. At to the coloful meaning, they are differnt though. ( If they are all the same in every aspect, there must be one giving the way). Basically, '套上’gives more imagery and vividness. And this, you know, counts a lot in literature. If somebody always uses words like 穿上 in their works, they'll lose the readers. Besides, with this kind of vivid discription you may portray and shape a visual character.

套 is"Put a wreath in something”。 I think 套上 is more "casually" and "roughly", compared with "穿上”: " 套上外套"., and 套上also has a meaning "put a wreath on animal or in something" ，套上马车had one's carriage hitched up，套上马鞍saddle. 套上绳子make a rope round something, like "在狼的脖子上套上绳子" .. "穿上”is more put on or wear. "穿上内衣”. you can say 穿上外套，穿上T-SHIRT，But you cannot say 穿上马车。。。

套上 for T-shirt kinda of shirts you need to put on them from your head. 穿上 Anything except 套上

Yes. In your example "穿上" and “套上” are interchangeable. I can't think of any difference between the two words when they mean "put on".