A Recording Studio is simply an environment to allow for the creation of multimedia.
This media can take several forms (or combination of forms):
- Music
- Sounds
- Video
- Graphical
- Presentation
Here is a link to a more detailed definition of a Recording Studio (WikiPedia):
http://en.wikipedia.org/wiki/Recording_studio
Audio Engineering is the means by electronic equipment to record sound.
Here is a link to a the WikiPedia definition of Audio Engineering: