What is the difference between FYI and JFYI?

Solution 1:

Generally "simply for your information," unless context indicates otherwise.

Solution 2:

JFYI is an acronym standing for "just for your information". You can think of it as being a kind of preemptive response to the question "Why are you telling me?". For example, in the exchange:

"I'm not going to be home tonight."

"Why are you telling me?"

"Just for your information."

Your paraphrase of "simply for your information" captures this better than "only for your information" (which might be ambiguous with another reading whereby you mean something like "for your eyes only").

As to the difference between FYI and JFYI, I'm not sure there is a big one. The former is more conventional and JFYI seems to indicate that giving the information is something of an afterthought or may not be very important to the recipient. The "just" seems to indicate that you are giving the information merely for the information's sake, and not for the sake of having the recipient act on it. There is less of this indication with FYI.