Learned from a professional machinist but I did not have any other schooling or training. He taught me well enough to bring me into the shop he worked at in a tool and die shop in a forge.
I started on kick pins and started my first die impressions a month after I started. They gave us a blue print, template, and a manual lathe...
The dies were for 4,000 ton and 6,000 ton presses. Not sure of the weight but we were talking around 24" diameter and larger and 10" thick. The 2.5 ton jib cranes were often barely able to lift the raw dies. I only worked there for a year before I embarked on my current career since 1999. I have my current career because of my machining skills.
I have acquired the skills to properly operate a lathe, mill, shaper, and surface grinder and most of the tooling associated with those tools. I've learned to set up jobs on all types of machines in conventional and unconventional situations.
I can measure accurately with all the standard types of measuring tools found in a normal machine shop.
I've been successfully completing projects and customer jobs in my hobby shop for near 30 years. I do not feel embarrassed to consider myself a machinist.
The one place I'm lacking is math skills. I'm constantly learning.
I don't see any reason to limit the term machinist to people who took formal training.
I think
@Investigator said in his OP that apprenticeship is a valid equivalent to formal training for being qualified to use the title of 'machinist'; you sound like you've done the apprentice thing, even if it wasn't officially called an apprenticeship.
On a general note:
The most abused term is 'Engineer'.
My father did an engineering apprenticeship in the London dockyards and the UK merchant navy in the late 50s. He was 2nd Engineer in the 60's (didn't make it to Chief, he never was that ambitious; I know where I get that lack of ambition from
). He was definitely an engineer, not a fitter, machine operator or maintenance mechanic.
In Germany though, due to his lack of undergraduate degree, he wouldn't have been entitled to join a professional body and so could not would have been recognised as an engineer. Not sure what title he'd have been entitled to.
These days in the UK, anybody can call themselves an engineer and often do. Heating maintenance and repair workers call themselves heating engineers.
Now the fella I use is great. He's reliable, quick, very knowledgeable and has never failed to fix any issues and has occasionally spotted the early signs of trouble, potentially saving me quite a bit of bother and cash (he's always keen to explain everything before getting the go-ahead). Great guy and I'm happy to pay his very reasonable invoices. You can tell how much I value him by the fact that at Christmas, I drop off a bottle of Laphroaig (usually Lore) at his house.
I'd never say this to his face, but he's not an engineer. He's a great, smart, skilled repair and maintenance technician.
I won't call myself a 'Software Engineer'. If the majority of the projects I worked on followed best practice and were as rigorously developed and had the level of automated testing that they ought, I probably would but a combination of 80% deadline pressure (and yeah, those setting those deadlines, seem very slow to learn that their priorities are arse about face: "To go fast, you have to go well" as 'Uncle Bob' Martin says) and 20% my own learned bad habits mean I don't feel I'm entitled to yet. It's getting better where I work, so maybe in my 29th year of being paid to design/write software, I'll finally feel comfortable to give myself that title.
All of which ramble is to say, titles are ways to get paid more and little more beyond.
Sure, be cautious about how you present yourself and your skills via any title you give yourself but don't let it affect how you feel about yourself.
