Subrelations are breakdowns between eVar dimensions. … Yup, that's really about it.
Correspondingly, correlations are breakdowns between prop dimensions.
Why the distinctive names? Mainly because of legacy reasons. props were introduced in Omniture SiteCatalyst (the predecessor of AA), followed by eVars. Both had their own allocation and persistence settings, which had implications on breakdowns. Thus, their breakdowns had different names to make sure analysts knew what they were breaking down.
These days with Analysis Workspace, AA has basically removed all limitations in breakdowns between props and eVars. You can break down one dimension by the other (e.g. eVar by prop or prop by eVar) with little consequence. So there's really no need to know the difference between subrelations and correlations any more.