I believe the term "homeless" was adopted in part to avoid more pejorative terms like "bum" or "vagrant". However, there may be some differences. You may not notice the majority of the homeless. They may very well hang out in libraries, coffee shops, and park benches, but these folks may be people with no mental illness or addiction, victims of the economy, or a restrictive housing supply. Alternatively, they may be people with personal health (including mental health) challenges that do severely impede their ability to work (or just cope with the world), but they have no immediate outward appearance of distress or addiction, and they don't pass out on city streets or, worse, intimidate, berate, threaten, stalk, harass, or assault fellow citizens.
The term homeless has come in the vernacular to refer to the people I referenced in that last sentence as the "homeless", almost to the point where the word is detached from home and less. It means a severely addicted and mentally ill person who lives on the street.
I don't know which one is increasing. I've lived in SF my whole life (SF, not the Bay Area, I took urban muni routes home from middle school), I'm in my late 40s, and I've never seen it so bad. I've always been a big public transportation taker, but I'm less enthusiastic about it now. What were occasional bad moments in the 80s and 90s have become an every other ride experience in some locations, and the lows are starting to get really, really low.