Probably both. It's known that the shirt and hat seen in the dispensary were found in his car. mother said that all she knows is that JJ was wearing a pair of shorts and tennis shoes. There has been nothing reported about the location of the dress shirt/pants that he was wearing at the student union.
There's definitely a lot of details that are either confusing or outright conflict, and some of them have come up here, with no real resolution. Like whether JJ was supposed to meet the advisor on Tuesday or Wednesday. The director saying that he missed a class at 1 p.m. doesn't narrow it down unfortunately because classes on all four days started at 1 p.m.
What is meant by missing class for "several days." Earlier I said that Tuesday would have been his third class, but that's probably wrong; based on the class schedule, it seems likely he had classes Mon-Thurs, so Tuesday 8/24 would have been day six of classes in the fall session. Does several days mean three days? Or more? It's something that should be relatively easy to verify.
With all due respect to the family, JJ "making plans" or "not being depressed" does not rule out or make self-harm impossible. There was similar disbelief and accusations of coverup/mishandling when authorities announced their findings that Kori Gauthier had jumped from a Mississippi River bridge or that Saniyya Dennis had done the same at Niagara Falls.
That said, I'm not taking any definitive side here. I just hope that LE can retrace JJ's steps and complete an investigation and the results are accepted by the family/friends.