Different Types

1) Repricing Risk
Also known as interest mismatch or gap risk.
This risk is associated with the timing differences in the maturity (for fixed rate) and repricing (for floating rate) of positions
For example fixed rate loan for a long period when interest rates are low but funded by short dated liabilities whose interest cost has risen sharply

2) Yield Curve Risk
Parallal shifts - the change on all maturities is the same
Non Parallel shifts - different maturities change by different amounts

3) Basis Risk
Arises from imperfect correlation between changes in interest rates from different market sectors (ie the spread changes)
In the futures market this has a specific meaning. Basis is the difference between the cash price of the underlying asset and the futures price

4) Optionality Risk
A lot of instruments contain optionality
Loans where borrowers can prepay balances