I seldom disagree with Marcel, but I do (a little) on this one. In residential construction, in a typical floor structure, a beam that is installed so that floor joists rest on top of it is typically called a girder. A common example is where a 20’ wide structure is too wide to have joists that span the entire structure. A “girder” beam is typically installed down the center and the floor joists rest (bear) on top of it. Usually joists will overlap above that girder.
In a ceiling structure, again… too wide to use ceiling joists that will span the entire structure, a beam is typically installed down the middle. If the joists rest on top of the beam… it’s just called a beam. If the beam is installed so that the bottom of the beam is flush with the bottom of the ceiling joists, it’s called a “flush beam”, since the bottom of the beam is flush with the bottom of the joists, creating a flat ceiling.
Constructions terms vary by region in North America.
There are glossaries produced by the American Institute of Architects and other professional organizations that attempt to create standard terms. I was trained by the American Brotherhood of Carpenters that adopted formal terms from architectural and engineering organizations, but I have had severe misunderstandings when dealing with newly-graduated architects and engineers because some colloquial terms are deeply entrenched in the building trades and academics don’t always prepare students to deal with that.
What it all comes down to is that it doesn’t matter what you call it, as long as everyone involved in the conversation understands what you are all talking about. If there’s some question about terms, that’s a good time to use photos and annotation in the report.