A physical adaptation occurs when an organism develops a physical trait that is especially honed for helping them survive in their environment. For this trait to be considered an adaptation (as opposed to a mutation), it must be passed down to the organism's offspring via DNA. Physical adaptation occur in response to stimuli in the environment, and, importantly, is a long-term process. Thus, while one organism may develop a certain trait, it is only an adaptation if subsequent organisms of the same species continue to improve on this trait.
Almost all physical features on organisms in the natural world are a result of adaptation. For example, in human beings, the eyes are specifically adapted for the world in which they live (e.g., seeing with the aid of light); in contrast, bats "see" with sonar because they do not have the aid of light. The rate of physical adaptation varies wildly depending on the organism; it took millions of years for human eyes to develop to their current level of ability, where as viruses can adapt in a manner of days to changes in their environment.
A behavioral adaptation is an adaptation that involves no physical change in the organism, but does involve a noticeable change in an organism's patterns. Behavioral adaptations can occur much faster than physical adaptions, and they often only affect a smaller subset of the organism's population. However, even if the behavior only affects a subset of the population, behavioral adaptations still must be passed down to offspring in order for it to be classified as an adaption. An organism simply changing its behavior due to a temporary change in its environment is not considered an adaptation.
One of the best examples of a behavioral adaptation is how certain animals (e.g., dogs, cows and chickens) allowed themselves to be domesticated by human beings. This is advantageous behavior for those animals because it ensured them a continued existence, whereas many animals that failed to adapt to the presence of human beings went extinct. However, it should be noted that there is a difference between a behavioral adaptation and a "learned behavior." Behavioral adaptations must be inherent in the animal, whereas learned behaviors are taught. For example, a cat's ability to hunt is considered a behavioral adaptation because cats know to hunt without the guidance of another cat; however, a human being's ability to make tools is considered a learned behavior because humans would not know how to do this without being taught by another human.