Spot Curve

This is used for discounting when you are receiving payments in the future.
Also known as a Discount Curve.

A spot rate is the discount rate used to calculate todays value of a future cash flow.
Converts a future cash flow to todays value.
This is used to convert a future cash flow to its present value.
this interest rate is called a spot rate or discount factor

Theoretical Curve

This is an "implied" or "theoretical curve
This is a sequence of such risk-free rates with varying maturities.
This can be used as a benchmark for pricing instruments

Important

It is called the zero volatility spread because we have not allowed for volatility. We assume the rates are deterministic.
This is the best curve to use when determining the relative value.