Adams is an extremely common name. Everybody seems to have a legend about being descended from the presidents. A couple of old ladies in my family were absolutely convinced about it and tried to get into the DAR. I set about checking it out even though it didn't sound right. My Adams people came from N. Ireland a couple of hundred years after the presidents' ancestors came from England. My ancestor WAS related to a John Adams but he was a farmer in Washington County PA. My grgrgrandmother's sister was given to tall tales.
That doesn't necessarily mean you aren't related especially since they came from Massachusetts. Do you know how long they have been in this country? You're just going to have to work your way back and find what you can about the presidents' family. You are right. It is difficult to find out anything about them. You can go back but not forward. Maybe the DAR or some of those other clubs can help you.