1) Studying at a good institute can really make a difference.
2) Studying at good institutes can really make a difference.
Do both the sentences carry the same meaning ?
It sounds like these sentences are both stating generic facts, to any difference is negligible. I would say they mean the same thing.
If you moved away from the generic truth into the realm of personal experience, however, the implications are different.
Studying at a good institution can make a difference.
Studying at good institutions can make a difference.
Both sentences are saying that the quality of the school can make a difference. Because this simple truth can be applied to one or to many, it doesn't really matter which way you say it.
I studied at a good institution, so I got a good job. I studied at good institutions, so I got a good job.
In this case, the second sentence implies that you studied at more than one institution, so you wouldn't want to say that unless (a) you had studied at more than one institution, and (b) all of the places where you studied would be considered "good" institutions.