In all creative endeavors there is a phenomenon called the anxiety of influence–the angst arising from the suspicion that your ideas are supposed to be your own, but that they are in fact related to, or derivative of, those that have gone before.
Among grad students in the sciences, this can set up a tension between advisor and graduate student.
Now tension is not necessarily a bad thing. In measured doses, the anxiety of influence pushes you forward to do something new. And one hallmark of good science is novelty.
Don’t let it worry you too much. It is expected that a grad student, at least in their first year or so, will be doing something closely related to your advisor. Hopefully, you two will be discussing lots of ideas. The last thing you want to do is constantly dwell on ownership of ideas.
It is your advisor’s job to recognize and nurture your insights. In most cases, those insights will constitute a “rediscovery” (the nature of 99% of all insights). In other words, you will have made a cool and valid connection that someone has made before.
Some small proportion of the time, you will make a connection that is the genesis of a new, truly cool idea.
Both represent progress, in that you are learning to think creatively.
After a time, you will even begin to recognize which is which by the way your advisor reacts. A “rediscovery” will illicit a warm smile (“progress!”, your advisor thinks); the genuine, new, cool idea will involve more expressive body language.
At some point, the anxiety of influence magically disappears. This event is often associated with your first paper, or the corpus of your dissertation.