MySQL is free and open source, was originally developed by a company that incidentally ended up being taken over by Oracle.
MySQL came way after the popular RDBMS of the early days - MS- SQL Server and Oracle who were the most popular (besides Sybase). MySQL was part of the Open source trend and thus became popular among developer communities and also part of the LAMP webapplication stack.
To answer your original question it is developed using C,C++, with yacc (yet another C compiler) for the compilation of the SQL scripts. I am not sure why this matters to you.
They are mostly similar. Besides the price factor (where MySQL scores), there are other differences - Oracle has a better support model, more features and reliability/maturity (having been around for way longer).
Oracle also works well with the other plethora of tech offerings from Oracle and considered enterprise grade, while MySQL is a great choice for small and medium companies.