Colloquially at least in the south the difference between a rug and a carpet seems to be movability.
Difference between rug an dcarpet.
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.
Main difference the main difference between rug and carpet is that rugs are an artistic way of covering the specific area of the floor adding style to the same whereas floor to floor and wall to wall coverings are called carpets.
What we call carpet is a floor covering that stretches from wall to wall and is affixed to the floor.
The size difference can be put in the following manner as well.
In some countries both words are the same and have no difference but in some other countries they are entirely two different terms.
Although rugs do the same a rug is entirely not the same item as carpet.
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.
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.
In other words a rug is less than 2m 6 5 feet in length.
Considering rug vs carpet there is steep difference between durability utility and portability of both the products.