Yes, they do have a lot of overlap in meaning. In this context,
appropriate is the appropriate word to use.
👁 Wink ;)
If you are describing something that is the right thing/the suitable thing to use or do in the situation then it is the
appropriate thing to use or do. A
proper schedule would be one that was printed out on a neat sheet of paper, rather than being scrawled on the back of a cigarette packet - both could be
appropriate, depending on the circumstances.