Hi Inexperienced.
Many would say one week for introductions isn't long enough. Believe me, I know. I spent more than a year trying to make an addition work here but it just didn't. Not only were there real fights but also stress induced sterile cystitis. I ended up having to re-home the cat I was trying to add to the family. It broke my heart but I had to do it for her health and happiness.

You might want to keep the two cats separated still when you cannot supervise.

In general, though...If one cat keeps going back for more, it is most likely play.

Is there vocalization of a really nasty sound going on before they pounce each other? Do they circle, arch their backs, put their hackles up, lay their ears back?

Usually, the difference between fighting and playing is apparent, but if you are inexperienced you may not realize the difference. What I describe above is usually true fighting. Circling, hoping sideways, going back for more, peaceful sharing of space between the romps, no blood being drawn or wounds being produced, it is probably play. Cats will growl and make some noise when they play but when they fight, good golly you might think you have a demon screeching in your home...you can usually tell the difference between fight noises and play noises.