Is there a difference between non-target schools?

Absolutely. School "prestige" isn't binary yes or no, people will still have heard of schools like USF/MSU and they will have alumni on the street, or people in the same athletic conference (for example, MSU students could reach out to other B10 alum). A totally random school no one has heard of absolutely hurts you and IMO nearly becomes a must-transfer situstion.

There’s definitely quality non-targets (think large state schools or very good LAC’s) where there’s some IB alumni, investment clubs etc.

and then there’s extreme non-targets. The school I went to had a student body of 1,000. No finance club, and the only alumni to even work at a bank is at JPM back office. Northwestern mutual is literally one of the most sought after positions at the career fair. When going to one of those schools, it’s extremely hard because you have no one to guide you. No professors that even understand what IB is and how you would get there, a career office that’s useless and so on

University of Wisconsin Madison is a solid non target though. Our banking club sends people to bulge brackets frequently. It's definitely better than MSU. Wisconsin Milwaukee is pretty ass though you're right all the retards go there

There’s absolutely a difference. Most people mentally bucket schools into something along the lines of excellent, very good, good, respectable and never heard of it. You’re a lot more credible coming out of a state flagship than directional state.

If you are choosing between non-target options, you want to go to a non-target with a big alumni base that gives you the easiest path into the industry via networking (much more painful to try and get non-alumni to pick up the phone). 

The non-targets with the largest alumni bases are the ones that attract a ton of kids from suburban new jersey, long island, DMV, etc. (think Indiana and Penn State). These kids are more likely to come from families where parents are white collar professionals that tell kids about finance jobs, and / or know people from their high schools and friend groups in the industry. The more people targeting IB, the more that get jobs, the larger the alumni base. 

There's a reason why these schools place 50+ kids a year into IB despite having the same academic reputation as say Wisconsin or Michigan State. It's not like some VP from Harvard is looking at an Indiana resume and saying "wow, Kelley, this kid is definitely smarter than the University of Minnesota kid". They just have way more students interested in IB to begin with because of the demographic pools they draw from, which then becomes a self-fulfilling prophecy as alumni pull people from their school through.

Almost every big state school will have an investment club like Indiana and Penn State, from Rutgers to OSU down to Iowa. The difference is that Indiana and Penn State draw from a much larger pool of students interested in IB, and push more kids through to finance every year as a result.  

Yeah it does. Someone said it above - people like to to bucket schools, but in reality it is a spectrum. I went to a non-target with alum at most top banks and as a result I was able to get interviews at said banks. 
In short, recruiting at each bank is typically segmented into three groups: diversity pool, target school (varies by bank) pool, non-target school pool. The non-target pool is basically a referral system and so having alumni in the industry is still crucially important for getting interviews. 

How about Caltech/CMU/Hopkins? What is the level of difficulty breaking in from these?