It is true that cats and tigers are related, though distantly. Tigers and lions are actually more closely related than cats and tigers would be. Felidae is the biological family of cats. A member of this family is referred to as a felid. The most familiar felid is the domestic cat. However this family also includes all other wild cats, even big cats like the tiger.
Extant felids belong to one of two subfamilies. The first is known as Panterinae and includes the tiger, lion, jaguar and leopard. The second is known as Felinae and includes the cougar, cheetah, lynx, ocelot and the domestic cat.