These taxes are for paid family leave and paid medical leave.
Should I just check the other box? or maybe the state an local deductible taxes box?
if I do, will they be counted as tax money I paid?
Does it really matter?
it matters if you are itemizing and declaring state and local taxes.
These taxes, WAPML and WAPFL (Washington Paid Medical / Family Leave) are deducted from the employees W2 and are listed in box 14 and would be categorized under "Other". Some companies put the amount on their W2's and some do not. If these deductions are included in box 14, does TurboTax use them in the calculating taxes owed/due or are they just superfluous information?
No, box 14 information does not affect federal tax calculations.
Some of the items you may find in box 14 affect your state return and that is why there are specific codes for some items. Since Washington does not have a state income tax, your box 14 entries do not affect your tax return at all.