Earplugs go into the ear similar to earbuds, but are squishy and meant to be rolled thin so you can get them in a bit further (then they decompress halfway inside your ear and fill in the gaps). If you push them in too far I imagine they can damage the eardrum, which could cause tinnitus.

After trying earplugs myself a few months ago, I decided it was too risky to sleep with them due to the pressure I felt in my ear (the one against the pillow) when I lay on my side.