Independent living for seniors can refer to a number of different housing options, ranging from an active adult community to senior apartment complexes, as well as independent living wings of assisted living communities. There are generally some planned activities, and many offer transportation to shopping and doctor appointments.
There are apartment complexes that are designed specifically for seniors. Units have been designed with seniors in mind, so there are grab bars in the bathroom, emergency pull strings, door handles instead of knobs, etc. It's like living in your own apartment, but all of your neighbors are seniors. There are some community activities, though maybe not to the same extent as in an active adult community.
Some of these apartment complexes are HUD subsidized for low-income seniors. You must qualify every year by submitting tax returns. Your rent is determined based on your income. If this is something you are considering, you should submit your application sooner rather than later, especially in the Bay Area. If a facility has an open waiting list, waits can be 3 years or longer!
Another model for independent living is a community that also has assisted living, usually in another building on the same campus. Those in the independent living section do not need assistance with the activities of daily living (ADL's) such as bathing, dressing, toileting, eating, and transferring. In some of these facilities, you can go to the common dining room and eat with other residents. Activities in the community are open to everyone. One advantage of this model is that you can start out in the independent living section, and if needed sometime in the future, simply transfer over to the assisted living section. No having to start all over making new friends and getting used to a new community.