They are two separate items. If you are receiving the $1,000 Child Tax Credit, then you are also getting the $4,050 exemption. However, the exemption does not add the money directly to your refund.
The $1,000 is from the Child Tax Credit. The CTC is a tax credit that will first reduce any tax liability that you owe and then, if you qualify, you can get the rest as a refund into your return in the form of Additional Child Tax Credit. So, this credit can add money directly to your tax return.
The $4,050 is from your child's personal exemption. The IRS allows everyone to have a personal exemption of $4,050 (this is in addition to a standard deduction). When you claim a dependent, you get to have their personal exemption in addition to your own. however, this exemption only reduces the amount of income you pay tax on - it does not "give" you $4,050 in your refund.
Example: Your income was $20,000 for the year and you are single with one dependent. Instead of having to pay tax on the full $20,000, the IRS allows you to first take a standard deduction of $6,300 and then also a personal exemption of $4,050. Since you have a dependent, you also get another exemption of $4,050. So, now instead of paying taxes on $20,000, you only have to pay taxes on $5,600 ($20,000 - $6,300 - $4,050 - $4,050).
So, having the $4,050 personal exemption for your dependent can help lower your tax bill by lowering the amount of income you have to pay tax on. Of course, there is the change it might not benefit you at all if you already have more deductions and exemptions than income.
