Asking the difference between Semi-Automatic Rifles and Semi-Automatic Hand guns is like asking the difference between Cars with Automatic Transmissions and Trucks with Automatic Transmissions: There are going to be plenty of differences, even in the transmission mechanisms, but Automatic Transmission will provide the driver with the same features regardless of a vehicle (you do not need to change gears, for this analogy).
Automatic and Semi-Automatic only refer to the nature of how a gun fires and reloads. It has nothing to do with any other nature of the weapon or the amount of ammunition that be fed into the chamber before reload. The basic rule of thumb to go by is that:
1.) Automatic Guns are guns that, when the trigger is engaged, will fire until either the trigger is disengaged or all loaded ammo is spent, which ever happens first. These are illegal to own by civilians unless they were made prior to the date of the law going into effect (I believe 1987) and in those cases, they are extremely cost prohibited (limited availability and licensing both make a hefty price tag).
2.) Semi-automatic Guns are guns that, when the trigger is engaged, will fire exactly one bullet (if loaded) and will not fire until the trigger is disengaged and reengaged. However, no effort is required to load firing chamber with a new bullet if there are still available rounds in the clip/magazine whatever. This is the broadest term as it can refer to hand-guns (generally all handguns are semi-automatic) and rifles, some of which are civilian versions of military fully automatic weapons that are designed to be semi-automatic (again, cannot buy new Automatic weapons at all).
3.) Non-Automatic are guns that must be manually reloaded after firing all chambered rounds.
For classification purposes, there is no difference between semi-automatic hand guns and semi-automatic rifles from the point of view of what is semi-automatic. It's one trigger pull, one bullet fired, rinse and repeat. One problem with laws as written is that while it is illegal to modify a semi-automatic weapon to be full automatic, it is not illegal to add attachments that will effectively change the firing nature of the gun. The device known as a "bump stock" that was used to make the weapon used in the Vegas Strip shooting fully automatic was not (at time of writing) illegal because it is classified as an attachment, not a modification. This may change in the near future as it is a rare issue, though it is hitting some stone walls (from what I've gathered, it does allow people who suffer from nerve damage to fire a semi-automatic rifle.). This works by using the recoil of the gun to re-engage the trigger (disengaged by the recoil) without the shooter moving his or her finger, effectively simulating automatic fire (stressing once again, this is not changing the semi-automatic nature of the gun. It just lets physics of a fired weapon pull the trigger for you).