Is this aggression or playing?

I have a 2 year old Australian shepherd (male), and a newly (less than a week) adopted 7 month old Australian shepherd/ Alaskan malamute mix (female) and there both fixed. The first day I brought her home they got along great, they even slept together. By day 2 and so on (this is day 4) they’ve been “playing” atleast sometimes it looks like playing and other times it looks like fighting. They’ll sniff each other a lot, follow each other around and lay around/ take naps together, and then when it’s time the puppy wants to play she’ll try to initiate it by bitting or nipping at my other dog and he responds by bitting back at her. It doesn’t seem like there biting down hard because neither one of them has yet to yelp or whine in pain but it looks intense at times. It seems like most of the time they bite each others fur but sometimes they get the skin. I’ve checked both of them for marks or cuts but it’s almost impossible to see anything with how much fur both of them have. My Aussie on occasion will show his teeth at her and seem very aggressive which he’s never done before but then they’ll also chase each other around back and forth like that for 5-10 minutes before one loses interest and they act like it never happened. I’m worried as she’s obviously a puppy and isn’t as socialized but he is , the puppy is going to training classes soon but they haven’t started yet and if this is true aggression/ fighting what are some things I can do to prevent it/ stop it.