Antique means more than 100 years old and semi-antique mean between 50 – 100 years old. In some cases an “antique rug” is just more than 80 years old. An vintage rug is more than 40 years old and some dealers use this expression instead of “semi-antique” rugs.
Rugs and carpets from the 15th-18th centuries are almost never called “antique” but are described by the century where they are considered to be made. A rug made in the mid 19th century may be called mid 19th century or circa 1850 but seldom just “antique”.