Although the duties will vary depending on the particular clinic, the two positions really come down to education and training. Veterinary Assistants are people who have worked around animals, are comfortable with clerical duties, and are willing to perform other tasks (dog walking, cleaning kennels, feeding, holding animals still for the doctor, etc.).
Veterinary Technicians on the other hand are usually trained, often certified to perform more than just basic tasks. They often will collect blood/stool/urine samples, prep animals for surgery (shaving), and even perform small procedures such as cleaning wounds and bandaging. They may also still do some of the tasks an assistant might. Because they have these skills, techs usually make more than assistants.
If the clinic you're considering is hiring an assitant, you should probably expect the pay to be an hourly rate... probably in the neighborhood of $8 - $12 per hour (depends a lot on where you live in the country and just how in need the clinic is).
My brother in law is a veterinarian and I used to work for an animal pharmaceutical company.