Answer
A cup is sensible or even mandatory to wear in (organized) sports where getting hit in the genitals is a real risk. Apart from the very real pain a hit there can cause, it can also cause very real damage.
A jockstrap - unless used to hold a cup in place - isn't necessary.
Some use them instead of underwear. Many don't.
Answer
A cup is necessary to protect you from getting hit in the testicles during sports. A jockstrap can hold the cup in place. Some are made just to support the genitals while you work out, better than normal underwar would.
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