Yes, they say that about both Moderna and Pfizer. I had a reaction to my flu shot this year, for the first time. It started an hour or two after the shot. First, my arm ached. Then everything began to ache. I developed a low grade fever and headache, too.
Felt shitty all night, but by the next afternoon, it was gone. So at least if I get something like that, I'll know what to expect.