What is a cat with small face and long tail that big not house cat?

You're describing a lynx.

Here's why:

* Small face: Lynx have distinctive, small, triangular faces with tufted ears.

* Long tail: While their tails are not as long as some other wild cats, they are longer than a house cat's tail.

* Big, not house cat: Lynx are much larger than domestic cats, and they are wild animals.

There are several types of lynx, including the Canadian lynx, Eurasian lynx, bobcat, and Iberian lynx.