To be broad here: Can Players use Ability Score Modifiers to add to their checks?
For example: can someone make a "Strength" check. (Not an Athletics Check) to, perhaps, break open a chest with force.
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This is information explained in the basic rules, but I may see where you've got a disconnect.
If your sheet contains precalculated modifiers for skills, those scores are based on your ability modifiers. If a skill is based on Dexterity, for example, its modifier is probably your Dexterity modifier plus, if you're proficient, your proficiency bonus. In fact, by the book, a skill check is an ability check. That's why the rules will usually refer to Strength (Athletics); you are making a Strength check with possible proficiency from Athletics.
You can certainly make an ability check that isn't related to a skill. For example, lockpicking is a Dexterity check. There is no Lockpicking skill. Instead, proficiency with thieves' tools would apply. Likewise, a check to see if you remembered the face of someone you passed on the road would probably be a flat Intelligence check.
In either case, you would add your ability modifier (+2), not your ability score (14).
Saving throws are not ability or skill checks. There are officially three kinds of d20 rolls in 5e: Ability (skill) checks, saving throws, and attack rolls. Each kind is subject to its own rules.