Blues goes deeper than a simple, single musical style; it spread north from New Orleans up into Chicago; sideways right through Creole zydeco and the later swamp pop of Louisiana and on into Texas. It has swept into almost everything we can hear.
Just a quibble here, but the blues spread outward from the Mississippi delta, Clarksdale, Indianola, Sunflower, etc.
Alan Lomax (? the folk documentary guy) helped preserve and promote the blues up north. Elvis and Jerry Lee popularized it here at home. The British musicians of the 60's, Stones, Clapton, Led Zep picked up on it, stole it, modified and made it even more popular....as you say,most people do not know they are listening to it when they hear Cream, or The Animals or Van Morrison.
I'm from the south. Lived in Clarksdale. But the blues came to me via Led Zep and the like. They were influenced most by the hardcore delta blues like Robert Johnson, Bukka White, etc. Those are the blues I like. A guitar, maybe a harmonica, rarely a drum kit.