If they're both having fun and no one is getting hurt when they play roughly, I wouldn't worry about it.
He doesn't really reliably know sit or down because he's not able to do it as a single behavior. It's all connected with whether or not you have a treat. People often make the mistake of doing things the same way every time. As an example, standing right in front of the dog, facing him with one hand on their waist every time they ask for a sit. Then when they ask for a sit and they're not standing right in front of their dog, he doesn't sit. They think he's being stubborn. But the fact is that dogs don't generalize worth beans. And this standing in front of the dog has become a part of the cue. "I sit because when she stands like that with one hand on her waist, I get reinforced." So then when the person stands sideways and a little distance off without their hand on their waist, the dog is confused.
They are so intuned with our body language that they notice tiny little things, even if our mouth is open or closed. So, it's important to vary your position to the dog, vary locations, mix things up, take a treat from a pocket one time, from the counter another time etc. Unless it is singled out from all these other variables and the dog reliably sits no matter what the circumstance, he does not really know sit.
What I would do then, with the sitting and down is to try capturing the behavior. Read about clicker training a little bit and prime him to the clicker. Or you can prime him to a word. But I really like the clicker because it's so distinctive sounding. Teach him what it means that click = treat every time. When he just happens to sit on his own, have that thing handy and click/treat. Or use a word you don't use for anything else. Just keep doing it.
He has learned that by your having the treat in your hand, that that is part of the cue.
Since capturing behavior depends on his choosing when to sit or just happening to sit, it may take a little longer. You can, in addition try something else. If he sits when you have a treat in your hand, let him see it but close your fist around it and motion for him to sit. Hold your hand to your side. He'll be looking at it, waiting for the treat. Have a treat in your other hand too and behind your back. Bring that one around to give him the treat. Do that a few times. Then try some out of your pocket, never giving him the one in the hand you're luring with. Then eliminate that treat and try. Lure into the sit and bring a treat from a different place. Vary the place. Get him use to the fact that he will not know where the treat is coming from. A clicker is useful with this. It lets him know what he just did....that very second which was what earned him the treat...which may take about 3 seconds to get. Try to eliminate the lure as soon as you can. You can make it more subtle and into a hand signal. Down the road, try using the hand signal by itself without the verbal and visa versa. Mix it up.
Then once he's reliable, skip a time of reward. But don't be in a rush to eliminate the treats. Keep reinforcing the sit. Practice the one position for a bit then try a different distance from you...just a few steps back. Don't change things in a huge way at first. Then turn to the side a little....a different room, use a slightly different body position. Squat down and ask for a sit. I'd get the sit up and running before bothering with the down. Once he gets onto the idea that treats come from different places and they don't necessarily come every single time (that's only when the behavoir is very well learned) he will probably be able to learn the down better and everything that follows. He'll learn better how to learn. Let us know if you have problems still. Give it time, have patience. He's still guessing what you mean. Once he gets enough reinforcers for enough reps, he'll start repeating that behavior. Keep your criteria low and easy for him at first...he doesn't have to sit for long. Gradually let him sit a tad longer before he gets a treat. Set him up so he's not apt to mess up. Make it easy for him at first. Short fun sessions. End on a good note with something he's good at. If he does pretty well, don't push your luck. End with some happy praise, a treat and some game. He'll be so much more into learning if he has fun. Good luck.
