WordPress integration – API

Hello,
I am new to the wordpress, thus I might ask a really simple questions. In fact I read many articles and googled but could not find the answer on simple question. Is it possible to integrate WordPress solution to my site using wordpress API? I am not interesting to install it in separate domain. I just want to provide my users possibility to write posts from their Accounts and show these posts on the web site. I saw many posts how to write plugins for wordpress, but my question is totally different. I would like to understand if it is possible to integrate some features of wordpress like for instance you are integrating Google Maps or Google places into your side. Or it is not possible and you should use something like Blogger API from Google?

Thank you for all upcoming feedbacks.