With teams only allowed to scholarhsip 27 of 35 rostered players, that means a minimum of 8 players are walk ons.
All colleges have open try outs. Most are a sham and the kids don't really get much of a look. An invited walk on means that the coach is looking to work the player out with the team, probably all fall, not just for the 1 day open tryouts. A question you should ask the coach is, "does the invited walk on spot guarantee a roster spot?" If it does guarantee a roster spot, and Junior can't get cut, then there is very little difference between the scholarship offer and the invited walk on offer. Conversely, if the invited walk on spot is without a roster guarantee, I would have no expectations of making the team, just the opportunity to compete for the spot.
A scholarship comes with a guaranteed roster spot. He could still get cut, but that is very, very rare and usually involves a disciplinary problem.