Abilities checks are typically referred to as a 'strength check,' 'intelligence check,' 'wisdom check' and so on.
Abilities checks are rarely adjusted, as most 'adjustments' are highly ad hoc and have little basis in terms of their amounts or incorporation. The use of modifiers for abilities checks represents an attitude directed against the characters successfully acting in a reasonable manner.
It is never necessary for a player to make an abilities check where the action to be taken may be assumed to be automatic. For example, it is assumed that a character with a dexterity of more than 12 can be expected to catch an item tossed from ten feet away without the need to make a check, while a character with a dexterity of less than 8 would almost certainly drop it. The latter character would need to make a dexterity check, while the former character can be assumed to succeed.
Thus, checks are made when success is in doubt. Otherwise, they may be overlooked.
Extraordinarily difficult actions are handled by required several checks, one for each action taken. For example, a character attempting to jump a ten foot distance onto an opposing roof with little running room would first make a strength check to see if they were able to clear the distance; then a dexterity check to see if they successfully gained a foothold on the sloped roof. If the strength check failed, the character might make a dexterity check to see if they were able to grab the edge of the roof; then a constitution check to see if they had the will to hang on; then a strength check to see if they were able to pull themselves up.