I am new to cycling. I recently got Jamis Trail X with 27.5x2.25" tires. This is a bit hard (not easier) on city roads. I was thinking about replacing the tires with max 1.5" wide hybrid or road tires. I researched a little bit and learned that 27.5 is not actually 27.5 rim. It's 26.5" or 584mm in diameter. My question is, can I replace these tires with any 584 or 650b tires?
Yes, you can replace your 27.5 tires with 650b tires as long as they fit your current rim. You need to get the internal rim width (B on the next picture) and use the following table to see if you can use the tire that you want on that specific rim. As long as the combination of internal width (in mm) and tire section width (in mm as well), then you should be able to use a narrower tire. Keep in mind that the table is fairly conservative, but when it comes to safety, it's always better to do things properly to avoid personal injury.
My question is, can I replace these tires with any 584 or 650b tires?
as long as it fits on your rim, yes. fitting on your rim means that your new tire has to be wide enough for your rim. if this fits, so every 584 tire will be fine. how wide is your rim?