Almost without fail, questions on here about American high school end up getting a bunch of answers that begin with "At my high school..." or some variation thereof. We remove them because of our rules around anecdotes but also because they're very often wrong for the simply fact that what was true at Smithtown High School does not necessarily reflect what's true at Smithville High School. There's a couple of reasons for that, all of which contribute to an answer for your question.

First, although it may not seem like it, American high schools are fairly responsive to local needs and conditions. It's why, for example, there are high schools with agricultural sciences or courses in specific languages. This doesn't necessarily mean they're always responsive but it's more a case of course correcting a tanker than uh, something that's harder to course correct than a tanker. One of the reasons for those local quirks is that there really is no such thing as American high schools, per se. Due to the courts' and legislatures' interpretation of the 10th Amendment, education is a matter left up to the states and then there are certain matters that are left up local school districts (the concept of "local control.") Some states allow more flexibility than others - slightly less than half the states are textbook adoption states, meaning the state education department determines which textbooks and curriculum resources teachers use while the rest set standards and leave the decisions about textbooks, materials, etc. up local districts.

All states, though, set graduation criteria. While there are some differences between states, generally speaking, all states require high school level course work in English, mathematics, science, art, music, physical education, and a language (modern or Greek/Latin) - or what we think of as a liberal arts education. The reason for this continuity between states is mostly due to what's known as the "Carnegie Unit":

The unit was developed in 1906 as a measure of the amount of time a student has studied a subject. For example, a total of 120 hours in one subject—meeting 4 or 5 times a week for 40 to 60 minutes, for 36 to 40 weeks each year—earns the student one “unit” of high school credit. Fourteen units were deemed to constitute the minimum amount of preparation that could be interpreted as “four years of academic or high school preparation.”

The Unit was established as way for schools to organize time in schools for several reasons, key of which was related to Andrew Carnegie's announcement in 1905 to fund college professors retirement provided they were working at a "real" college. The way he and his organization determined a college was "real"? They only admitted students who were college-ready - that is, they had completed an accredited high school program that included a number of credits, or Carnegie Units. Over the first few decades of the 20th century, American high schools developed a fairly standardized day. This isn't to say they weren't before Carnegie, as they were; the "look" of the American high school had mostly taken shape by the 1890s, even though high school was only something a few young people, mostly white girls, did. Taking a full day or week of Carnegie Units, though - often described as core courses or subjects - wouldn't fill a student's entire daily schedule. The nature of non-core classes is where local flexible and career and tech ed comes in.

Back to my point about a fairly high degrees of local control and flexibility or what we've come to think of as "electives." At this point, it's important to stress that, despite a modern shift in messaging, the purpose of American public education has never been about preparing young people for the work force. A whole bunch went into the thinking behind the creation of tax-payer funded schools in every town but "teaching kids to to be employees" wasn't one of them in any meaningful way. To a certain extent, American public education is part of the whole "American dream" construct - the government provides a well-rounded liberal arts education to any child (which has expanded over time) who shows up and they can use that education to do whatever they want when they're an adult. This thinking helps us understand why most vocational preparation is at local community colleges or stand-alone business schools. At the same time, if a local community seems a specific need, one of the electives might address that need like the agricultural courses I mentioned earlier.

There were, though, other pressures to expand what young people learned at school beyond just the core liberal arts. Beginning before World War II, courses like Homemaking (which evolved into Home Economics later Family and Consumer Science) were common. As were technical skill courses such as automotive repair, woodworking, architectural design, etc. It's important, though, to stress these were offered based on student and teacher interest as there was no administrative mechanism to speak of to force children into particular courses or classes. There were, though, social mechanisms and local decisions shaped by racism, classism, sexism that would result in particular students being encouraged to take particular courses or registered without their consent. These classes, though, generally speaking fit with the idea of a "well-rounded" liberal arts education - learning about the home and/or working with one's hands wasn't about a future job. It was more about being an educated young person.

There was a formal structure, though, for supporting teachers of these technical courses: The Smith-Hughes Act of 1917, which was the first authorization for the federal funding of vocational education (now known as Career and Technical Education). Smith-Hughes would later be reauthorized as the Carl D. Perkins Act of 1984, later the Perkins Vocational and Applied Technology Act (Perkins II) in 1990, Perkins III in 1998, Perkins IV in 2006, and Perkins V in 2018. In some states, vocational and technical courses were already offered as electives because there was a local need and students enrolled (or were enrolled.) In others, Smith-Hughes and Perkins offered funds to expand what as already offered. The Act also contributed to the rise of guidance/career counseling in schools but again, it's voluntary. That is, students who got "mortician" on a career placement or proclivity test were not required to enroll in mortician school.

After all of that, let's take a closer look at your question. First, vocational education at the high school level is still going strong. The Vocational Industrial Clubs of America Inc. (VICA), now known as SkillsUSA was founded in 1965 and supports thousands of high schoolers across the country to develop workforce skills. In addition, more than 30 states have created intermediary educational agencies to offer vocational and career training to students, taking the burden off of local school districts. In many cases, students attend their local high school for half day and then their vocational training in the afternoon, often graduating with both their HS diploma and a trades certification. One of the challenges is that when VICA was founded, it was possible to go right from HS to a well-paying job as the HS diploma was all that was needed for professional employment. In the modern era, a Bachelors degree is generally expected, meaning college has become more then norm for professional, technical jobs.

Regarding those stand-alone tech courses - this is where local decisions really matter. Some state still require FACS and some form of tech courses. However, in many cases "shop" has become computers, coding, 3D printing, etc. etc. In some places, administrators made the decision to cut the course - perhaps due to low enrollment - and use the classroom for something else. The basic gist, and answer to your question, is that technical and vocational courses at every high school in America has its own history.