Ignorance being shown here but would it be correct to say a "die" is a device (don't want to confuse the question by using the word "tool") that is used for forming material. I seem to be getting this feeling given the replies. Whether it be foam for a car seat (maybe that is a mould?) or something that becomes part of a manufacturing process that involves extruding, shaping etc?
Assuming some of this is true then a die maker may be the person fabricating this piece/part and he would develop a working part using one or more possible resources including his brain, drawings, prints and so on. This all sounds like a die maker is the one who does prototyping of manufacturing processing parts. If/when more than one "die" is required the original die is turned into a blue print and given to a Machinist who is responsible for removing unwanted material from a piece of stock rendering a part identical to the original die.
Now say this die is going to be part of an assembly that needs to be built. A tool maker would design and make a jig and/or fixture that would facilitate the production of the assembly that the die would become part of.
Is this a somewhat close overall view of the three different trades and titles?
Are (were?) most die makers also tool makers and vice versa? Is the title of "tool and die maker" one that a person has or is it more of a description for a type of machine shop. Sort of like all oncologists are hematologists IYKWIM?
Sorry for the ignorant rant. I completely missed the boat when I was 19 and spent a year working for a company that rebuilt machinery. It was on LI NY and they rebuilt and retrofitted machines in sizes from large Bridgeport Mills to gigantic gantry Mills for the aircraft industry. My job was wiring the control panels but I was much more interested in the metal and machinery than I was the electrical. This was when numerical control was just hitting it's stride. My one year there sparked a major interest in machining. Back then I remember seeing several dudes that seemed to have similar jobs but some spent all day working a machine and others would do some of that as well as other functions that I couldn't define. Not to be a smart ass but the latter were always a bit cleaner at the end of the day and we're usually standing with the brass when a customer was Cutting a cone to test a machine. Back then I though maybe they were part of the owner family or were professional brown noses that received special treatment but now I think these were the tool and/or die makers. The engineers never got dirty. Lots of dirty looks though
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I recently Googled this company. It was 38 years ago and they are history. Seems like they folded up in the late 80's and, from what I could gather, were involved in a half million dollar bankruptcy scam with another company trying to dupe the irs. I don't like cheats, liars etc. Unless they are getting a something over on the irs. Then I'll tip my hat.
Unrelated note. This job was the most brutal place for practical jokes. Guys washing their hands at the huge semi circle sink and another guy fills their pocket with Vactra 4. Guys taking someone's Street clothes, soaking them in water and putting them in the freezer. There was no limit to the things people would do to each other under the name of "practical joke"