OpenSSL is still used in many places as the SSL library for applications. Is it because there is great OpenSSL documentation? No. Is it because the OpenSSL API is intuitive? No. Is it because there is no good replacement for OpenSSL? No. Then why? Because it is most used SSL library in education, books and examples. We are trying to change that!
SSL vs OpenSSL
SSL is the actual SSL protocol as it is defined in a number of Internet standard documents, called RFCs. SSL and the successor TLS are well established as secure transport protocols. OpenSSL is an SSL library that implements (part) of that protocol. So in the question "SSL vs OpenSSL", or "OpenSSL vs SSL", the answer is: OpenSSL is an implementation and SSL is the standard it implements.
OpenSSL vs PolarSSL
PolarSSL is a direct replacement for OpenSSL when you look at the standards. If you look at our Features you will see similar items as on the OpenSSL feature list. The major difference is the way we make the code. We aim to help you make better applications. We provide as many documentation, examples and support as you need to be happy with the result.
PolarSSL does not yet offer an OpenSSL API. We try to make things intuitive and in most cases that means, doing it differently than the OpenSSL API. Functionally they do the same, but from a pure interface perspective, the OpenSSL API differs from the PolarSSL API in a lot of places.
OpenSSL vs mbed TLS
mbed TLS is the successor of the PolarSSL library. As such, the comments above on why PolarSSL is a good alternative for OpenSSL also apply to mbed TLS. Both are able to replace the OpenSSL functionality without any problems.