It's not a daft question it's something that causes a lot of confusion.
so let's say the care home charges £800 a week as it's basic rate for 24hour residential level care.
the local authority has done their social care 'care act' assessment and agreed that your mum meets their criteria for 24 hour care. They then complete a financial assessment and says of that £800 they will contribute £561.
a nurse then completes a nursing assessment and says that your mum also qualifies for the funded nursing contribution of £209.19 a week as you mum also has nursing needs above the residential care 'social care needs' the local authority has agreed she has.
The care home then says 'yes that's fine we also provide nursing care at a cost of £1009.19 a week (£800 residential rate + £209.19 additional nursing rate). **
nursing care is NHS care and therefore free at the point of access. So the NHS gives the care home the £209.19 directly to cover the cost of the healthcare the care home is providing on behalf of/ by proxy for the NHS.
that then knocks the bill back down to £800 a week to be covered by the person themselves/ the local authority.
** many care homes don't offer both types of care so if the funded nursing contribution is applicable then a residential only care home would either have to say 'no sorry - find a nursing home' or 'we think we can still meet the nursing needs with support from district nurses'.