Hey Nyle_Miura,
In my experience, larger corporations seek interns that are still in school, while smaller consultancies don’t pay much attention. If anything, I’d say smaller consultancies prefer someone who has graduated or is close to graduation so that they can train you then hire you. Nike is one of the bigger exceptions I’ve seen where in design they seem to prefer graduated students (conversely, they only accept current students in departments outside of design).
What sort of companies are you looking to join? It’s worth mentioning that you’re going to have a difficult time if you’re only reacting and responding to formal listings. I recommend making a list of 3-5 companies that you want to work for and be proactive in trying to open doors with them. People are much more willing to respond and react to your work when you pick them as a company you want to work for, rather than you picking the job listing and competing with thousands of other applicants flooding their inboxes. This route may take longer to find a job, but I think the upfront research of looking for companies will lead to a better fit for you and your future employer. On the topic of Jr. level vs. Intern, apply for both, it sounds like you’re open minded which is a good mindset to have!
Hope that helps,
Aaron