NCAA regulates the roster number to 105 until the first day of class. Teams can then add to their roster as they see fit, usually capping out at 125. In BYU's case, they've chosen to cap at 123.
The 18 players added on the first day of school are rostered players, and once they join the team on the first day of class are treated the same as any other player, short of scholarship money. They have a locker, get their laundry done, get cleats, shirts, equipment, free food, access to the SAB tutoring, help registering for classes, etc.

After the first day of school, the TEAM consists of 123 players. There is not a special 105 with another 18 looking in from the outside. Those 18 won't have their pictures in the program or online because pictures are taken during camp, but their names will be listed and a page online will be there for them, and they'll be listed on the All Time Roster when you search for their name. In the past few years, all eligible players in the 123 will also get a free trip to the bowl game, get the bowl gifts and a bowl jersey with their name on it.

What those 18 are working for is an invite to spring ball, when the roster again is cut down to 105 and will stay that way until school starts. Then, another 18 will be added and here we go again.

If you're a walk on and don't perform well academically or in football, you won't be invited to attend spring camp. Walk ons must keep an even higher GPA than other athletes to remain in good standing with the team.