The estrous cycle is the cycle of a non-pregnant female mammal that goes through a luteal phase and a follicular phase. Estrus is the period in which an animal will stand to be bred, and is part of the follicular phase of the estrous cycle.
An easy way to remember it is that estrous is an adjective and estrus is a noun. Thus, estrous refers to the entire cycle, whereas estrus just refers to the phase in which the animal can get pregnant.
Usage:
The female chimpanzee can get pregnant because she is in estrus.
The female chimpanzee can get pregnant in this phase of her estrous cycle.