I know there is 'voiced & unaspirated' and 'aspirated & unvoiced' categories of speech. I have heard there is a 3rd category. What is it?
Aspiration and voicing are not mutually exclusive phenomenon. You can certainly have a plosive that is voiceless (the more usual term for what you give as "unvoiced") and unaspirated (the one you are missing above), like [p] in English spin [spɪn], one that is voiceless and aspirated, like [pʰ] in English pin [pʰɪn], one that is voiced and unaspirated, like [b] in English bin [bɪn], and you can even have voiced and aspirated consonants, like [bʰ].
This last category is debated. Ladefoged (1971: 9) claims that such a sound "has yet to be observed", while Blust (2006) has shown that Kelabit, an Austronesian language, contrasts a series of voiceless unaspirated stops, voiced unaspirated stops, and voiced aspirated stops. For instance:
- /tutuʔ/ 'fall from a height'
- /tuduʔ/ 'seven'
- /tudʰuʔ/ 'salt' (all from Blust 2006: 314)
Vedic Sanskrit, Classical Sanskrit and accordingly a lot of middle Indian and new Indian languages have for each of five positions of plosive-articulation all combinations of voiced/non-voiced and aspirated/non-aspirated stops. The alphabet is structured accordingly, for each of the positions (from back to front: velar, palatal, retroflex, dental, labial) there are five sounds (examples from the labial varga):
- non-aspirated voiceless: [p]
- aspirated voiceless: [pʰ]
- non-aspirated voiced: [b]
- aspirated voiced: [bʰ]
- nasal: [m]
Regarding this, I don't really get Ladefoged's claim cited in @limetom's answer.