Are assisted living community and senior independent living the same?

No. One is assisted (help for stuff) and one is independent (no help for stuff).

Not quite. Assisted living is generally like a combination hotel and nursing home. Meals and maintenance services are provided along with medical monitoring.

In independent living, the seniors care for themselves, but have the option of monitoring and assistance.

Assisted living facilities provide people, not just seniors, with help where needed. This may include disabled people and senior citizens. The level of care will depend on the facility. It may include helping with health, safety and other issues, but normally don't have 24 hour medical care. Senior independent living would have transportation, laundry facilities, possibly dining, and some type of living arrangement (apartment). Usually, no medical care is provided, and seniors are free to come and go as they please.

Assisted living service is the best option for elderly who are not getting proper home health care. With home care services patient can live independently and happy.

No, they are not the same, although some locations will use various words to try and make centers sound more marketable.

Assisted living will normally have much less freedom on individuals living there, more assistance in living.