The correct English term for this is "Bonus points"
Basically, what you are describing is a bonus above and beyond what they would normally get in that situation. Whatever the individual systems call it, in addition to those names, they are "bonus points"
You can see this reflected in the rules of the various gaming systems mentioned in the other answer. (all emphasis is mine)
Fate points are described by their game system as:
Fate points give players the ability to take a little bit of control
over the game, either by giving their character bonuses when they feel
they need them, or by taking over a small part of the story
In Pathfinder, the use of Hero points are described as follows:
Using Hero Points Hero points can be spent at any time and do not
require an action to use (although the actions they modify consume
part of your character's turn as normal). You cannot spend more than 1
hero point during a single round of combat. Whenever a hero point is
spent, it can have any one of the following effects.
Act Out of Turn: You can spend a hero point to take your turn
immediately. Treat this as a readied action, moving your initiative to
just before the currently acting creature. You may only take a move or
a standard action on this turn.
Bonus: If used before a roll is made, a hero point grants you a +8
luck bonus to any one d20 roll. If used after a roll is made, this
bonus is reduced to +4. You can use a hero point to grant this bonus
to another character, as long as you are in the same location and your
character can reasonably affect the outcome of the roll (such as
distracting a monster, shouting words of encouragement, or otherwise
aiding another with the check). Hero points spent to aid another
character grant only half the listed bonus (+4 before the roll, +2
after the roll).
Extra Action: You can spend a hero point on your turn to gain an
additional standard or move action this turn.
Inspiration: If you feel stuck at one point in the adventure, you can
spend a hero point and petition the GM for a hint about what to do
next. If the GM feels that there is no information to be gained, the
hero point is not spent.
You will notice that they specifically call it a "bonus" when hero points are used in the manner which this question is asking about such points.
In D&D4e the rule system is even more explicit calling everything either a modifier bonus, or a feat bonus, or a power bonus etc.