If I claim '1' on my W-4, that amount is equal to ~$4050.00, spread over the year, and I believe is counted toward taxable income, and is taxed on your paychecks. If I were to claim '0', is that same money just 'saved' until I do my taxes, and then it is taxed anyway at tax time, before my refund? My question is; is the money in my pocket the same (at the end of the year), whether in my paychecks over the year, or at refund time? thanks!
The number of exemptions you claim directly translates into an amount withheld from your paycheck for taxes. A larger number means less withheld, a smaller number more. 0 would be the most possible withheld. You can see Publication 15 for the table of how much would be withheld based on your paycheck, and how the number of exemptions affects this.
This number does not in any way affect your tax due, however. As long as you have withheld at least as much as you owe in taxes, you'll get a refund of whatever extra is withheld; if you have less withheld than you owe, it's possible you might owe a penalty if you owe more than $1000 and don't meet any of the exemptions (for most filers, paying as much in taxes as you paid last year, or 90% of what you owe this year).
If you end up withholding more than you owe, you're basically giving the government an interest-free loan until tax time; and if you have less withheld, you are getting an interest-free loan (unless it's > $1000 and you owe a penalty which is basically that interest).
Note that the specifics here are appropriate for the 2017 and earlier tax years, but will change in 2018 with the change in personal exemptions going away; this hasn't been finalized yet, however. If you're considering making a change right now, I would wait until late February when the IRS should have new guidance and perhaps a new form W-4.
Well, the actual question you posted is a bit vague (pronouns with antecedents that have to be inferred from context), but the answer to the question I think you're trying to ask is "yes".
When you fill out a W-4 form, that tells your employer how much to withhold. Your employer takes much they expect to pay you, subtracts how much deductions you claim on your W-4, and calculates taxes based on that. So for withholding purposes, whatever deductions you claim on the W-4 will not be included in your taxable income.
However, when your taxes are calculated at the end of the year, your taxable income will be calculated based on what deductions you are actually eligible for; W-4, amount withheld, etc. have no bearing on the total tax liability calculation, only on tax paid calculations. All the money that was deducted will be applied towards your taxes owed. If your withholding was larger than your tax liability, you get a refund. If it's less, you owe money.
In some circumstances, if you owe too much money, the IRS will apply a penalty. And if you are owed a refund, that is money that you've basically loaned to the IRS interest-free. But putting aside those two factors, the total amount paid is not affected by the W-4, only the time that it's paid.