What is the difference between present value and face value? What is the difference between present value and face value? 
When I search this question on Google is says they're the same in some cases and different in others. It says they are the same when the market interest rate is the same as the contractual interest rate. 

I need help understanding what this means. I do not understand the difference between these  types of interest rates, etc. 
And also does this have anything to do with discounting vs. coupon bonds, etc?
Suppose the face value of a bond is $M$ and its interest rate is $\tau$. This means it will pay $\tau \cdot M$ interest every year (other periods are also possible) and at the end of its run (its maturity) it will also repay the face value $M$. Government bonds are usually sold in auctions. Whatever ends up being the market price is considered to be the present value of the bond. Using the cash flow you can also calculate the yield of the bond. If and only if the face value and the present value are equal the yield will be equal to the interest rate.

For an example see the US treasury's website. Click on bonds to see face value, interest rate and maturity, click on the bond serial to see its price (present value).

Further reading here. (Link copied from a comment by @Jamzy .)