Merging 2 independant objects at their intersecting faces

I was hoping to merge 2 cubes at their intersecting faces/edges like so:

There are numerous ways.

For a simple shape you can use the boolean modifier

You can also use the snapping options (magnet icon on header) to modify the size of the small cube then join both objects together with Ctrl+J and create the faces to join the faces.

I see, so it basically creates a copy of the object merged into the object you are using the boolean modifier on, but only the vertices on the inside or outside based on the settings, then you can delete the original and the added vertices remain, that’s more what I am looking for, the latter isn’t quite so good of an idea s i’m looking for a way to merge a completely sculpted human head model onto a body model, so recreating faces on a few hundred vertices sounds like a headache

and i knew the ctrl + J hotkeys ;D