A detailed understanding of the role of Active Galactic Nuclei (AGNs) is required for investigating topics in galaxy formation and evolution and it is critical to be able to reliably differentiate between AGNs and non-AGNs in samples of galaxies. As a method for separating AGNs and star-forming galaxies, the BPT diagram is of particular interest because it uses commonly available optical emission line ratios and is already widely used in studies of narrow emission line galaxies. However, it is not well understood what exactly determines where an AGN lies along the AGN branch of the BPT diagram. Furthermore, AGN spectra, especially in SDSS, will be contaminated by emission from star-forming regions. In this work, we study the line ratios of “pure” AGNs—BPT AGNs which have had their star formation contributions empirically removed by matching AGNs to star-forming galaxies with similar host properties. We find that such pure AGNs populate the full range of the AGN branch, suggesting that mixing between star formation and AGNs does not account for the extent of the observed (pre-correction) AGN branch. Instead, we find that the narrow-line regions of AGNs have a wide range of physical conditions: variations in ionization parameter and metallicity can account for much of the diversity of pure AGN line ratios. Based on all the available emission lines, we also find that pure AGNs can be separated into three types: Seyfert 2s, Soft LINERs, and Hard LINERs. The Seyfert 2s separate from both types of LINERs primarily in ionization parameter, whereas the two types of LINERs mainly differ from each other in the hardness of their radiation field. Despite their distinct characteristics, multiple types of AGNs may coexist at the same BPT line ratios.