What is the difference between a grounded tip soldering gun and a grounded soldering gun?
A grounded soldering iron will have its body set to ground.  Generally if a soldering iron power plug has a third prong (the ground prong) then the soldering iron will be grounded.  This helps prevent shocks because any current leakage will be directed towards ground and not towards you.

A grounded tip soldering iron has its tip set to ground reference i.e it will be set to the ground reference of your power plug - again check for the third prog in the power supply.

If your son is going to work with ICs and other delicate electronics then a grounded tip soldering iron is the one you want.  The grounded tip will ensure that any excess charge will be channeled away instead of into the chip thus preventing ESD (Electro-Static Discharge) damage.

If you just need a soldering iron to solder copper pipes in your bathroom then either kind is fine.