It is not a matter of being more or less professional, it is more a matter of more or less formal. Compare the two sentences:
- Dell makes computers.
- Dell manufactures computers.
They mean precisely the same thing. If I spoke the second sentence, my hearer, if he noticed at all, might think I was being slightly too formal or pretentious. If it were printed in a formal report, the first sentence might be thought to be slightly too casual -- but probably not. It's just not that big a deal.
The most common term used to refer to the manufacturer of an automobile on government forms is "Make". As in "What is the make and model of that car?" In news reports on television it is more common to hear "automaker" rather than "auto manufacturer", simply because "manufacturer" is more formal. Not more professional.
I think I agree with @rsegal's comment in that it would be less common for a single craftsman to be referred to as a manufacturer (although ironically "manufacture" comes from a French word meaning "make by hand"). I have a relative who makes custom jewellry; she works alone. I would probably not use the word "manufacturer" to describe her operation, even though she is a professional (meaning she earns her living doing this activity). Pehaps in this sense size matters, but nobody would hesitate to say that a large company makes a given product. But it is not less professional to use "make".
I would not hesitate to use "piston maker" in a professional context.
However, a "supplier" did not necessarily "make" the item. Many "suppliers" merely bought the item from the "manufacturer" for re-sale. A piston maker is automatically a piston supplier, but not the reverse. Typically, "supplier" is reserved for a wholesale operation, not a maker or manufacturer.