Definition of set
In English, there are two types of three of a kind. On the one hand, there is a "three of a kind" (three cards of the same denomination, i.e. three of a kind) and a "set". When we talk about a set, we mean that the three of a kind has been built with the pair in one player's hand. For example, if you have A5 on 5-5-4, you have three of a kind. In English, this is called a "three of a kind". But if you have 55 on 5-4-2, now you have a set because the three of a kind was built with pocket pair.
A set is worth more than a set of three!
If you have 78 on 7-7-2, you have a set. However, your hand will be dominated by 7-9 or 7-T or 7-A. In other words, several better 7s. If you have 77 on 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 comes down 7-7-5, you know that it's possible that a player has a set. But on 7-5-2, yes, a player could have a set, but it's a more subtle hand and less obvious than when there's a flop double.