QGIS Field Calculator functions

$area is the area of the current feature. It's a numeric variable.

area is a function which takes a geometry, and returns its area. This geometry could be any geometry, not just the current feature.

You could say that $area is the same thing as area($geometry)

Some examples - you could use area (the function) to get the area of the bounding box of the feature, for example...

area(bounds($geometry))

.. or the area of the feature after applying buffering

area(buffer($geometry,0.01))

You could replace $geometry in those examples with a different geometry completely, for example you could lift gml or wkt from a field and use that as the geometry.