Are asteroid complexes and types the same?
Yes they are basically the same. The original asteroid taxonomies were defined from photometry (brightness) in a few filters such as the Eight Color Asteroid Survey of Tholen (1984). This resulted in asteroids with similar slopes being grouped together into the main complexes or classes. Once we got more detailed spectra of asteroids subtle differences between sub-members of e.g. the S-complex showed up and so the large complex was broken into more sub-classes such as Sc, Sq etc.