all the above is correct.
keep in mind.....
I have worked on cars with owners who supply their own parts because they can get them 10-20 bucks cheaper.
they werent too happy paying double labour when the part fitted was incorrect.
have also charged others for hoist down time, whilst they reorganised the correct or missing part.
those people also not happy.
ended up costing more than the entire job would have.
some parts(if sold at RRP as they should), workshops make very little out of.
some, there is more 'meat' for them.
all comes down to the workshop and supplier.