According to the Laws of bridge, there are two types of adjustments when there is an infraction.
First, if a board is not played or not completed, then an Artificial Score is awarded, or in English we give Average, or Average-plus, or Average-minus. Examples: suppose your opponents accidentally look at the score sheet, so you cannot play the board, or there are twelve cards in one slot and fourteen in another, or someone is slow and you lose a board, or someone sits at the wrong table and it is corrected, but the bidding is different with the correct opponents, so the board cannot be completed. In all these cases the TD gives some form of Average, A+ if you are no way at fault, A if you are partly at fault, A- if you are completely at fault.
Second, if a board is completed and a score is obtained, then if the TD wishes to change the score because of an infraction, he is required to award an Assigned Score, or in English, he works out what would have happened without the infraction [giving the benefit of the doubt to the non-offenders] and that is the result on the board. There are complications because of the terms "likely" and "at all probable" and so on, but the basic idea is simple: the result obtained at the table is replaced by another one. Example: you double 4 slowly, your partner takes it out to 4 which makes, +420: the TD [or AC] reckons your partner's 4 was improper because of UI, so he adjusts to 4 doubled: he judges it will go one or two down, so he assigns the score of 4*-1 [benefit of doubt to the non-offenders], +100.
The distinction between the two forms of adjusted score is clearly spelt out in the Laws. The artificial type is covered by Law 12C1, which starts with the words "When, owing to an irregularity, no result can be obtained, ...". The assigned type is covered by Law 12C2, which starts with the words "When the Director awards an assigned adjusted score in place of a result actually obtained after an irregularity, ...". The distinction is clear.
Unfortunately, to apply Law 12C2 means the TD [or AC] has to do some work and apply some judgement. Because of this, incompetent and lazy TDs have found it easier to give Artificial scores when they are not legal, and an Assigned one should be given. The practice is so prevalent and TDs and players have got so used to it that many of them do not realise it is just wrong. Another reason that the practice is so common is that in quite a sizeable chunk of cases the correct method and the wrong method come to much the same thing: assigned scores quite often are around the 60% mark at the end of the day, so people do not see a problem.
However, there are a number of hands where this practice leads to unfairness for one side or the other, and as a result it is a totally undesirable practice. For example, take the case I quoted earlier: if the save of 4*-1 is one no-one else finds then the pair concerned will be getting a 100% board after a correct and fair adjustment: giving them a 60% board [which A+ normally translates to] means they have been cheated out of 40% of a top by the idleness or incompetence of the TD.
It is not always the non-offenders who suffer. Suppose a pair reaches a cold 6NT making +1 for a 100% board - but they have misinformed their opponents. With correct information their opponents will find a better lead and take one trick. However making 6NT is a 90% score only. The correct assigned score would be to give the offenders 6NT making for 90%: giving them A- would be cheating them out of 50%.
The ACBL has got into an unfortunate position with its interpretations of Logical Alternatives and "at all probable" and "likely" and they occasionally give A+/A- because their interpretation means there is no score they can actually assign! Hopefully they will sort it out one day, but until they do, there will be some artificial scores given in NAmerica on this basis. The good news is that it is very rare that they are given for this reason, and it is probably only the top ACBL TDs who actually understand when it happens, and even then it normally works out to an approximation of what a European TD would assign [trust me - it does!].
The EBU/WBU have specific regulations that cover special cases when again A+/A- can be given. This means that this is an acceptable practice. They do so in the areas of fielded psyches and fielded misbids [see the article Adjustments for fielding], and use of illegal conventions.
Leaving these special cases apart, in most cases that a result is obtained, a TD is required to assign a score by nominating a result. Many don't, but it is because they don't know any better or they could not be bothered to follow the Laws.