Do vet assistant make more money than vet technician?

No, not in general. Veterinary assisting is an entry level position and in most states veterinary assistants are more restricted in the types of duties that they can perform. Veterinary technicians, however, are commonly required to have a degree in veterinary technology and to be credentialed (much like human nurses). For this reason, veterinary technicians are usually paid more and allowed to perform more duties with less supervision.