Definition of set
In English, there are 2 types of three of a kind. On one side, there is the "three of a kind" (three cards of the same denomination, therefore, a three of a kind) and a "set". When we talk about a set, we mean that the three of a kind was built with the pair in a player's hand. For example, if you have A5 on 5-5-4, you have a three of a kind. In English, it sounds like an "three of a kind". But if you have 55 over 5-4-2, now you have a set because the three of a kind was built with a pocket pair.
A set is worth more than a three of a kind!
If you have 78 out of 7-7-2, you have a three of a kind. On the other hand, your hand will be dominated by 7-9 or 7-T or 7-A. In short, by many better 7s. If you have 77 out of 7-5-2, now no one can beat your three of a kind because you can't share it with anyone else. That's why you have to be careful not to give the same value to a set as to a three of a kind. Also, from a psychological point of view, a set is a more discreet hand. If a flop falls 7-7-5, we know that it is possible for a player to have a three of a kind. But on 7-5-2, yes, a player could have a set, but it is a more subtle and less obvious hand than when there is a double on flop.