It is interesting how the definition of words change with popular usage. In the original meaning of the word, a mechanic is one who understands the entire mechanical system from concept, to design, prototype, production and maintenance. A mechanic is not a parts changer, but a well-rounded master of machines. In the purest form of the word, engineering is a dicipline of the mechanic, as is machining and the maintenance of machines.
A technician, on the other hand, is one who specializes. There are medical technicians, elevator technicians, lab technicians and obviously car technicians. A technician is a specialist at one small portion of an entire system, whereas a mechanic has a broad understanding of the entire system.
To bolster that assertion, here's what Webster's Dictionary has to say:
Technician: Specialist in the technical details of a subject or occupation.
Mechanic: An artisan. A machinst or one who repairs machines.
Before engineering was recognized as a profession, those who engaged in the science of designing machines were called mechanics. Mechanics generally not only designed the machines but were equally well versed in the making of them. James Watt was one such mechanic and reading books written a when he was alive, he was called variously a mechanic or an inventor. Those who ran his steam engines were called engineers as defined by Samuel Johnson's "A Dictionary of The English Language" published in 1767.
To get a better idea of who a mechanic was, in the truest meaning of the word, I recommend reading "Memoirs of the Most Eminent American Mechanics" by Henry Howe, published in 1840. The "engineers" of the Industrial Revolution were not called engineers back then, but mechanics.