Same Character or Not?

Take for example:

繁体：傢具  -> 简体：家具

繁体：家庭  -> 简体：家庭

In simplified, both "家" are identical despite there different origin. Does this also mean both "家" are considered the same character?  Or put another way, could I describe the 家人 as 家具的家，人口的人？

I'm sure this question applies to other characters as well, just no others come to mind.