It looks like the spring and fall internships are rare when I see job postings. Yet there are a lot of grad students on LinkedIn who get internships during Fall or Spring. Is it because they made networks/connections during a conference and somehow end-up getting an "invite" to interview? Think of ML Research Intern at Apple, Research Intern at Google or Applied Scientist Intern at Amazon. Apolgoies, if my question sounds dumb :)
it's because they are citizen
That's one probable reason. I have also seen international PhD students doing Fall/Spring internships