You only have six ability scores -- you have modifiers for each ability score (like strength) and modifiers for each skill (like athletics). When you create a character, you'll choose initial values for each of your six abilities (either by rolling dice, or using point buy, or using the standard array). The race you choose will modify some or all of those values, and as you level up you'll be eventually able to increase those values.
Your score in any one particular ability determines your modifier for that ability (subtract ten, divide by two, round down).
- Example(STR 17): 17-10, divide by two 3.5, modifier = 3
Your modifier for skills are equal to your modifier for the relevant ability, plus your proficiency bonus if you're proficient in it.
So for example, let's say your starting strength was 15 at character creation, plus 2 from half orc. So at level 1 you'd write "17" as your strength and "+3" as your strength modifier. Your proficiency bonus at level 1 is always "+2", so your athletics modifier is either "+3" or "+5", depending on whether you chose athletics as one of your initial skill proficiencies.
Your skill modifiers are constantly "updated" to match the relevant ability modifier, so if later on your strength goes from 17 to 18, those +3 modifiers all become +4.