Other people have answered correctly but the details are interesting (and I’m sitting in an airport waiting for my plane to arrive so I have time).

In the big picture, people generally produce “the same” antibodies in that almost everybody tends to target the same places on a pathogen protein. For example, H1N1 influenza viruses have 6-7 places that antibodies preferentially bind to, and different people all target those same places. They’re called “immunodominant” sites, and immunodubdominant sites are less well targeted.

(Because this is biology, nothing is ever 100%, so there are occasionally people who don’t target one or a few sites well, or people who are particularly good at targeting sites that are normally subdominant. Studying these people and understanding why they do this is an active area of research.)

So that’s the big picture, but if you drill down and look at the actual protein sequence of the antibodies that are doing the binding, they are not typically the same. Other comments have pointed to somatic hypermutation as a cause of this, but even ignoring SHM, most people have very different sets of responding antibodies. Antibodies are originally generated randomly, and it turns out that there are many ways to find very similar solutions - there may be billions of ways to get an antibody that binds to H1N1 immunodominant site “Sa”, say.

So if you compare the sequences of antibodies that are apparently doing the same thing - even between identical twins infected with the same virus at the same time - you won’t find much overlap.

But, drilling down yet another level, you will find some some overlap. We call the overlapping sequences, that are shared between different people, “public” sequences, and those that are not shared “private”.

The ability to sequence antibodies in this way is fairly new, with tech that really started to become widespread in the last ten years, so we are still trying to get a handle on the ratio of public to private sequences. If you look at two people, they may share no sequences; if you look at 100, you may find a couple dozen clusters that various people share; if you look at a thousand, who knows? It’s starting to seem that a significant percentage of antibodies are kind of public - someone else out there has something like it; but most are not widely public - it might only be shared among say 5% of the population.

Again, this is an area of very active research, with groups trying to understand the significance and potential uses of public vs private sequences.