Typically, a person would rent an apartment while they were going to school or as the first place they stayed after leaving home for their first job. They might have even had someone (or more than one person) live with them to share the rent. However, some people remain living in the family home and never move from it.
It is not unheard of for people to purchase a home straight out of college or as they begin that first job, but having an apartment is done more frequently. When a home purchase is involved, it can be a new one or an existing one, depending on several factors such as the amount of down payment saved up, where the home is located, how soon they need it, and more.
Regardless of how people start out - apartment or home - they generally progress through a series of different ones as their needs, income, and family situation changes. Some people move between cities for employment reasons. Some get married. Some start families. Some have parents or other relatives move in with them as those people become less able to care for themselves. Some move about within the same city as their employment or income changes.
Nevertheless, people generally have a few different homes that they have lived in by the time they get to retirement age - more when their childhood homes are factored in. Over that time, they will have had homes they liked, and some they likely didn't care for as much. Perhaps they didn't one or two of them that well at all.
We'd like to think that people rented an apartment or purchased a home because it fit their financial parameters, was in a location that provided a commuting distance that worked for them, had amenities in the community or nearby that they appreciated, and generally had a layout that was to their liking. Of course, some people likely made hasty decisions just because they needed a place to live, or something unforeseen happened near them (a large retailer, factory, warehouse, or outside storage) that changed the appeal (and potential appreciation or value) of that home.
So, in the course of moving through life, many people identify a home that they like well enough to consider remaining in it forever and not looking for another one to replace it. Depending on their employment and whether moving for job-related reasons might be appropriate later on, people can come to this realization at any age. It's not just people in their 60s or 70s that determine that they have found their long-term ("forever") home. This can happen at any age, or it's possible it never happens - people just continue to live in the home they have later in life without liking it that much but resigned to keeping it and making the best of it. They figure that remaining put is easier (and likely less expensive) than moving.
So, the question becomes one of whether a new dwelling is needed or advisable - and for what reasons their present home doesn't measure up to what they need or require. If it's where it located, that can't be changed without a move. However, if there is something physical about the home - layout, features, condition, styles, colors, or finishes - we can change that as aging-in-place providers.
Throughout the past few decades, moving from home-to-home has been quite common, with the average person moving every five years. For many reasons, including the fact that we now are prepared to help people renovate and modify their homes as they age, moving may not be the best option for people.