Often I seem to find these two terms seemingly used to mean the same thing, though I do get confused as my brain cascades over questions around "Source, contents and container", as in "if it's coming from the grid then surely it must be fed in-to the battery/installation" and yet 'feed-in' seems to suggest feeding in-to the grid, which should be 'feed-back'.
Is there a standard?
Am I overthinking it? Probably.
It's just that we're not talking about sandwiches, where the mustard goes under the ham, or onto the ham, but the ham must be in the sandwich. Or is it like being "born out into the world"?