Since 'stress relief' is now an industry, there are so many ways of dealing with it.
The problem is that often somebody finds a way of dealing with stress that works because it is a distraction that works for them personally. Unfortunately, rather than focusing on the fact that stress relief is commonly dealt with through distraction it is presented as the specific task as being a stress reliever.
There are several basic ways to deal with stress.
This can be done with exercise as long as there is not a significant mental component (in the sense that you don't want to add to the stress or counter the physiological effects of exercise.)
Removing or reducing the cause of the stress. While this may not seem to be possible, there are often ways to reduce the cause when elimination isn't possible. The most common problem here is the "I have no choice." defense and until you realize that you always have a choice, you will not be able to address it from this perspective.
Chemically it can be addressed, though this should be avoided except in extreme cases, where there is clinical control, as it's an ideal breeding ground for addiction.
Exercise, sports, hobbies, creative endeavors, sex, dancing, etc.
Addressing the Symptoms
Chemical such as tranquilizers or CNS depressants (benzodiazepams, alcohol etc,) These tend to work fast and as already stated, unless there is control, can (not necessarily do) lead to addiction.
Removal of the stress causing task/situation. This is as before not always possible but there are often alternate approaches that stress will blind the subject to.
Some people thrive in a stressful environment. It is not a virtue though and shouldn't be thought of in that context. There is, therefore, no shame in not being one of those people. It often requires a good deal of strength to realize and accept it. There is a sociological pressure that creates an environment of rewarding those for whom deal with stress more easily as a virtue. It is irrelevant as problem solving is the issue and not the addition of unrealistic pressure. (e.g. if your a surgeon, you may have to deal with an extraordinary problem in the middle of an operation. Knowledge of the task at hand is whats needed to address this, not 'the ability to handle stress.')
These are the tools. It is a matter of how you use them for your particular situation. Every situation requires a 'hand crafted' solution. Anyone who says "All you need to do is...." is usually way off the mark.