My thought is that you haven't described the situation very specifically, but if you came up with an idea for a website with Feature Set {item1, item2, item3, . . . } and did all the coding yourself, you aren't plagiarizing anybody. You're just attempting to solve a problem someone else is attempting to solve too. The users will decide whom to do business with.

Trademark and copyright are distinct issues, but you haven't mentioned anything that would raise a trademark or copyright issue.