Regular skates is what I've taken to calling figure skates, especially to fathers of young boys. (And thanks to my friend Jan Tremer from the PSA for the tip.)
A couple of years ago I had 3 or 4 year old boy in a tot class, whose father had put him in hockey skates, and the poor kid couldn't stand up. So we told the dad, let's try figure skates. "Oh no," he told us. "Figure skates will make him gay."
I am not making this up.
There are three basic types of ice skates, and variations within those types. These are figure skates ("regular" skates), hockey skates, and speed skates. Each is engineered for the skills each discipline calls for.
For first time skaters your best option is, ahem, regular skates. Okay figure skates. These are characterized by a long wide (in relative terms) blade with points on the front end (the toe pick and toe rack), and a length that generally extends beyond your heel in the back. ("Patch" blades and dance blades are shorter to give greater edge control.) Figure skates are easier for most people because of their length and width (I know they look skinny, but hockey blades are skinnier, and speed skating blades skinnier still). You just have to learn to avoid the toe pick, but unless you routinely walk tippy-toe, this isn't that challenging for most people. Specialty skates include "patch" blades for compulsory figures, and dance blades.
Beginner figure skates have a smaller toe rack without a distinguishing large top pick. It is very hard for beginners to skate in a free style blade because of the large toe pick. Don't let a skate salesman talk you into it. I recently had a Beta-level student show up in a Phantom blade (a $300 high-end freestyle blade). Poor kid was tripping all over the place. I told her that she was in too much blade for her level and that she'd need to be careful, but apparently her uncle was an "expert" and he said this was the skate she needed. The following week she showed me how her uncle "the expert" had ground off the top pick. So he basically ruined a pair of $300 blades.
Don't do this. Get the skate your child needs, not the one that satisfies your ego. In fact, rental skates are fine through Beta, or even Gamma (Basic 5-6). Ask a coach to help you learn to choose rental skates with a decent blade.
Hockey blades, in addition to being narrower, have more of a rocker (the slight curve back to front along the length of the blade). They are also shorter, which, in combination with the deeper rocker, is what makes them hard to stand up in. It's always entertaining to watch the little first-time hockey kids lean forward and just keep tipping over because of the slippery curvy blades (this would also be me in hockey blades). Goalies wear a specialty blade. If your child can stand up in hockey blades right off the bat, hooray. If he can't, let the coach put him (or her) in figure skating blades, um I mean "regular" blades, just until he learns to balance. I promise, that if he turns out gay, this is not the reason.
Speed skates, of course, are much longer, and I believe have a negligible rocker. I've tried to skate in speed skates, but that long blade makes me feel like I'm glued to the ice. I've never had a student come to a beginning class in speed skates, but I don't know why you wouldn't. Don't take anything higher than Alpha/Basic 4 in speedskates. Don't try to go backwards. You cannot even do a three-turn in speed skates.
You can learn everything up to three turns in hockey skates; at that point the skills diverge (hockey players don't generally do three-turns, at least not on purpose, although it's possible). Most people who reach a free style (figure skating) or varsity (hockey skating) level can easily switch from one type to the other because they've learned what a rocker feels like and can compensate for the differences in the blades.
Finally-- skating is skating. As a beginner/developmental coach I have no opinion on what type of skating any given student ends up doing. I just want them to learn to have fun on the ice.