I have come across the word infrequent in the patient information leaflet for Prozac. When looking up the German translation of that word, I wondered what exactly is the difference between infrequent and rare?
First, the definitions:
Not occurring often; rare.
(of an event, situation, or condition) not occurring very often.
1.1. (of a thing) not found in large numbers and so of interest or value.
1.2. Unusually good or remarkable.
From the definitions, we see that both rare and frequent can both refer to something that does not occur very often.
However, rare can also refer to something which does not exist in large numbers, such as works of art or certain species of creature.
So you can say that supernovae are rare or supernovae are infrequent. However, while you can say that the Philippine Eagle is rare, you cannot say it is infrequent.
EDIT: As pointed out in the comments by @JasonBassford, when used to express frequency, rare would be more appropriate in more extreme cases.