A "note" can be much more than an aid to memory.
I might write a note to the milkman*, to ask for an extra pint of milk. I might write a note to my child's teacher to ask for a morning absence to visit a dentist. I might write a note to summarise the key points of a book. These are to help me remember, but they aren't "reminders" more of a "summary". An academic might write a note to a journal to be published. The key to being a "note" is it is like a short written letter, which might be written to remind you of something later.
(Not to mention musical notes, and bank notes)
On the other hand, a reminder need not be written. I can give a reminder to my child to take out the trash by speaking.
While a reminder could be in the form of a note, it very often isn't. While a note could function as a reminder, it could do lots of other things.
*Actually I won't because I haven't seen a milkman in about 30 years.