Three different products get called the same name, so here are the strict meanings.
Age-restricted housing means occupancy is limited by age under the federal Housing for Older Persons Act, which is the exemption that lets a community lawfully exclude families with children. For the 55-plus version, at least 80% of occupied units must have one resident aged 55 or over, the community has to publish and follow the policy, and you have to keep age verification records. Several states add their own requirements on top, so have a fair housing attorney confirm what yours demands before you advertise anything. Nothing gets "registered" in most places; the compliance lives in your documents and your files.
Active adult means age-restricted housing with amenities and no services. Independent living, used strictly, means age-restricted housing with hospitality services bundled into the rent, typically meals and housekeeping, often transportation and a full activities calendar. Assisted living means licensed personal care, help with bathing and dressing and medications. Your building with a piano and a coffee machine is active adult that a broker is dressing up.
No nurse is required for housing with no personal care, and pure independent living generally isn't licensed as a care setting, though that turns entirely on your state's definitions. Ask the state agency directly.
Smaller balance sheets usually get exposure through listed REITs that own senior housing, or through private funds and syndications, where minimums often start around $25k to $50k. If you do buy a building, budget two lines conventional apartments don't have: an activities coordinator's salary, and marketing priced per move-in rather than per unit, which in this product runs into the thousands.