There aren't many similarities between mutualism and parasitism, except for the fact that there are two or more creatures involved in the whole process.
The differences are many, the most important of which is the fact that mutualism involves two beings living in harmony, where they both have something to gain from that symbiosis. On the other hand, parasitism means that one being gains everything from its host, whereas the host is just being used, there is no gain for it in the whole process.
Hope this helps! :)