It’s more complex than it looks like. The body randomly creates many different antibodies against many different type of antigens. The one that’s able to bind on the antigen on the virus is the one that will start reproducing and creating millions of itself if necessary to fight the specific virus.

The two antibodies of the two different persons will be most likely be different. One of them will probably have a higher affinity towards the virus compared to the other person which will mean that that person may also fight the virus faster.

I can’t go into much more detail since I still haven’t been taught much about this topic yet.

Source: med student