...What do the terms grille and register mean?
A grille is a vent that does NOT have a damper.
A register on the other hand is a vent that does have a damper.

...What is a supply grille/register?
A grille/register is a vent in which the air is coming out of the wall, ceiling, or floor -- supplies air to the space.

...What is a return grille/register?
A grille/register is a vent which takes air from the space back to the fan or air handler.

...What is the difference between wall and floor grilles/registers?
Floor grilles/registers can support the weight of a person (extra bracing) while wall ones cannot.