CNA--certified nursing assistant is the title of a state-issued certification. Depending on where you get your training, it can take as little as a couple of weeks or an entire semester. Training can be inexpensive if done at a community college or cost big bucks at a private school A fortunate few are able to find paid training (minimum wage while in school) in exchange for a work commitment of 3-6 months. Then the pay jumps up to the going rate.
PCT--patient care technician--is the title of a job held by some CNAs. I've also seen this job referred to as PCA--patient care assistant.
LPN--licensed practical nurse--is a state-licensed position. Education typically last 12-15 months. The pay is higher than for CNAs, but so is the responsibility. LPN's are being phased out (or have been phased out for some time) of many acute care settings, but they are welcomed in long term care (nursing homes).