It may sound surprising, but it is not always clear what is meant by a "concealed hand" or a "concealed set".
Basically a hand is said to be concealed, if all its tiles excluding the winning tile have been drawn from the Wall. A concealed hand with a self-drawn winning tile is said to be "fully concealed". Other common synonyms for "concealed" are "private" and "independent". Note however that certain rules (e.g., IMS rules) might use the term "fully private" when they mean a "concealed hand" (i.e., the winning tile can be a discard). This can most probably be explained by the fact that the original Chinese term for a "concealed hand" is men qian qing, which literally means "fully concealed hand", while a "fully concealed hand" (in Western sense) is called men qian qing zi mo, which literally means "fully concealed self-drawn hand".
Similarly, a concealed set is basically a Chow, Pung or Kong, where all tiles have been self-drawn. Though concealed Kongs are placed above the hand and normally partially exposed, they are still essentially concealed sets.
The problems start with interpretation of Kongs as concealed triplets. Traditionally only concealed Kongs are considered as concealed sets (and comparable with concealed Pungs) while other kinds of Kongs are not. However, some rules consider all Kongs as concealed triplets, based on the fact that in any kind of a Kong at least three tiles have been drawn from the Wall. Other rules accept only concealed and claimed Kongs as concealed triplets (and comparable with concealed Pungs), while rejecting Kongs that have been promoted from melded Pungs.
This leads in a situation where some rules accept all Kongs in a concealed hand, while others accept only concealed Kongs, or concealed and claimed Kongs.
The concept of "concealed" is further complicated by the fact that some rules exclude all Kongs from a concealed hand, and often disregarding the way Kongs are generally interpreted in the rules. E.g., in Chinese New Style, all Kongs are considered as concealed triplets and accordingly allowed in Concealed hand (discarded last tile), but no Kongs, not even concealed ones, are accepted in Fully concealed hand. Here the emphasis is on the self-sufficiency of the hand: after all, even a concealed Kong informs other players about the contents of player's hand, and also deteriorates player's chances to go out, since four tiles of the Kong are unplayable after the declaration and cannot be used in other combinations.
The concept of "exposed" (or dependency) is confusing for the same reason. Acceptance of Kongs in patterns Exposed hand and Fully exposed hand depends primarily on the general interpretation of Kongs as concealed sets, so some rules accept no Kongs (disregarding whether they are concealed, claimed, or completed from Pungs) in an exposed hand (since all Kongs are considered as concealed sets) while others might accept Kongs promoted from melded Pungs (the ones not accepted as concealed Pungs by the rules), or all non-concealed Kongs (in case the rules acknowledge only concealed Kongs as concealed sets).
As in the case of "concealed hand", some rules (e.g., Chinese New Style) specify an exception to the general interpretation of Kongs and allow all Kongs in an exposed hand, even concealed ones. The emphasis is here in the lack of self-sufficiency of the hand. Melding four sets leaves a player with a single tile in the hand, and makes his game totally visible to the opponents. Kongs, whether concealed or not, are not different in this respect from melded Pungs or Chows.
Four Winds 2 lets you specify how the concept of "concealed" is used in scoring. The general rule for interpreting "concealedness" of Kongs is specified on the General option page of the Rules section, and exceptions to the general rule by using a separate Kong option for scoring patterns Concealed hand, Fully Concealed, Exposed hand, Fully exposed hand and Hidden Treasure.
Kongs Kongs as concealed sets
Bonus for the hand
Bonus for winning
Limit and Special hands Classical