To answer your question in short, No. The federal tuition credit is only applicable to reduce your federal tax payable and Provincial tuition tax credit is only applicable to reduce your provincial tax payable.
When you filed your personal tax returns, you are filing for federal and provincial. Assuming that you are in Ontario, your total tax payable contains federal and provincial portion.
Thus, you cannot apply provincial tuition tax credit to federal tax payable or federal tuition tax credit to provincial tax payable. As a matter of fact, the tuition credit calculation is different between federal and provincial. Thus, you will notice that the credit is not the same.
If you have a spouse or parent, you transfer the credit to them (there is a limit). If you do not use the credit, you can carry them forward. When you received your Notice of Assessment (after you filed your return), it will tell you how much unused credit that you have.
Thanks for taking the time to explain this for me.. I appreciate it! So when I file my income tax lets say in total it is 20,000 CAD so part of this tax goes to federal, and part of it goes to provincial right?