This is TOTALLY age appropriate, not a sign of being a bully, and very raaaaarely a sign of any kind of disorder. He'd only be a bully unless you didn't stop him, and teach him not to hurt people purpose. So you know...this kind of behavior varies in format (and comes on and out in different ways) for the next year and a half to two years. You might go 6 months or a year with no hitting/hurting...only to have it crop up again. Not because they've decided to be a bully, but because they've reached another developmental milestone. And then you start all over, coming at it from the new angle that they're working with. Each succesive time you deal with this problem, the social rules get laid down a little more permanently.
For example, at one, on timeout the partyline was "You HURT so and so. We don't HURT people. Hitting HURTS your friend. This is too hard, this is gentle. We need to be gentle with people."
At two on timeout it was "You HURT your friend, and you HURT your friends FEELINGS. What are you supposed to do when you're angry? Are you supposed to HURT someone or are you supposed to take a deep breath and count to five?" or "What are you *supposed* to do if they take your toy?"
At three it was "When is okay to hit/hurt someone?" (a: When you're defending yourself or someone else) or "When is okay to yell at someone?" (a: When there's danger, or they're far away.)
What we did at each stage was unilateral timeouts or go homes for hurting or throwing a fit. You hurt someone you go on timeout. Flatout. For every stage. Then we can discuss/model/teach, but it was the equivillent of slamming on the breaks, each and every time it happened. Then of course, you start teaching mental/emotional integration (aka what to do when you get angry, over excited, hungry, or even just FASCINATED with long blond hair). Those tools are the first ever, so be patient.
If we were in a playgroup type setting and it was an excessive force kind of thing (not intentionally hitting/biting/kicking/pulling hair/throwing sand/ because he was ANGRY...but hitting or knocking down out of joy/not paying attention/as a way to get attention/ just using too much force), or hanging out with family, this might mean a trip to the next room for timeout on the couch, or out of the playground for a trip to the benches. Whereupon we could model the appropriate kind of behavior...then come back and apologize and try again. If he did it again, we'd go home. He'd get the extra chance to try again with people who cut us some slack, knowing what was up...but he'd STILL go on timeout.
(Timeouts in our house aren't punishment, they're a way to remove oneself from a situation, calm down or evaluate something that went wrong. )
If he did it out of anger we went home. If we were amongst strangers, we'd go home. Obviously I (at the very least) would apoloise to the child and their parents. Just out of common decency. All parents who have a child 2 and over have at least been through the beginning of this stage. Most parents are just thrilled that you're actually working on this problem instead of ignoring it and letting your toddler beat on their kids because "he's just a baby" or "this is MY time out of the house". You run into both attitudes in parents (denial, or the inability of recognizing who is the child...aka we're responsible for them, not they for us)
Lousy time for ME...because it quite frequently meant we'd only get to be somewhere for 5 minutes and then we'd have to turn around and go home...and because I had to keep an eye on him at all times (not get caught up in conversation)...but if this was all about ME I'd have a babysitter.
Good luck, and best wishes for patience & consistency. The two hardest, but best things in your arsenal for the next 2 years.