Confusion about sanity testing of software

I have read several posts regarding smoke and sanity testing. All are almost confusing. Neither explaining them clearly,just repeating the matter except some two or three posts and based on that two or three posts i concluded that following is the formal process:

Smoke testing(generalized health checkup)---then--> Sanity Testing(checking some main functionalities to somewhat more deeper level)(Specialized health checkup)----------------then--------> Functional testing(full functionality checking at deeper levels)

Am i right in above concept?

I have confusion regarding when sanity is performed. Smoke is performed when build comes very first time. But when sanity is performed? Is sanity is performed only after every smoke OR it is performed every time build undergoes some change(i.e. even when smoke is not performed because smoke is performed only first time build comes) OR in both cases?