Nursing homes and care homes are very similar to each other but the difference is that nursing homes have registered nurses working in the nursing homes to care for the residents.
So in nursing homes the residents get much better care from registered licensed nurses whereas care homes have carers that are not registered nurses but do receive some good care but they don't have as much experience with health related issues for treating those patients for those issues and have to have other nurses take care of the residents.
Usually a nursing home is much better for long term residents who need long term care especially if they have things such as dementia since the registered nurses can better care for the patients with those conditions.