The size difference can be put in the following manner as well.
Difference between rug an dcarpet.
What we call carpet is a floor covering that stretches from wall to wall and is affixed to the floor.
This is the reason you cannot flatly say that a rug is just another word for a carpet and you cannot use these words as a synonym to each other.
The word rug has come to mean a smaller item as in an area rug that is around 4 feet by 6 feet or less while the word carpet reflects bigger items as in an area carpet that are over 4 feet wide and 6 feet long.
A rug is smaller than a carpet.
A rug vs carpet rug and carpet are terms that are used interchangeably.
Rugs on the other hand tend to be smaller than the square footage of the room by a lot or a little and are not affixed to the floor.
Colloquially at least in the south the difference between a rug and a carpet seems to be movability.
In other words a rug is less than 2m 6 5 feet in length.
In america a carpet is a floor covering that is laid wall to wall and rugs cover only a small area or they are area specific.
People call a wall to wall covering as a carpet and prefer to call smaller pieces that are either kept in the center of a room or below a bed as rugs.
Although rugs do the same a rug is entirely not the same item as carpet.