I am surprised to find this question as a simple web search will return millions of hits with good comparisons, history, etc.
This goes back to UNIX itself and the storied history it has. One could almost ask the question “what are the differences with UNIX?” There are many “versions” of UNIX, both proprietory and open sourced. You can see the history starting back in 1969 with Bell Labs and Ken Thompson and the rest of the group designing an operating system. It later branched with BSD and now has many variations including Solaris, HP-UX and AIX.
While a student, Linus Torvalds wanted to improve an academic version of UNIX called MINIX. The version he started posting was called Linux.
To say Linux and UNIX share the same Kernel is not exactly correct. First off, which version of UNIX are we comparing. It is more accurate to say that it is Unix-like. They both use monolithic kernels which handles process control, networking, and peripheral and file system access. It is just that they are all writen, changed, modified, adapted by different groups. Many commands are common across most of these implementations, however, parameters and information returned may be slightly different to very different.
Usually a question like this would get you an RTFM. But I think people have become more polite on the web these days.
But, still, dont ask a question like that at work without at least having researched it on your own to an extent, and then phrasing it in the form of a discussion. “So I read that Unix and Linux have so and so difference, but I dont really agree with that, how would you describe the differences?”