Liquidity Risk is a situation when an individual investor, business, or financial institution fail to meet its short-term debt obligations. This happens due to several reasons like inefficient market, shortage of income due to lack of buyers.

If you as an investor purchase a bond with a longer maturity date and you receive an extra amount as a return to your investment then it is known as a maturity risk premium. Maturity risk premiums are provided by the company to boost investment in bonds for r period and compensate investors for taking risk through bond.

It's quite clear to understand the difference between Liquidity Risk and Maturity risk premiums :
Liquidity Risk is an event of capital loss whereas maturity risk premium is an amount given by the company to the bond investors.

Liquidity Risk occurs when the asset may lower its value due to short term event of cash requirement and Maturity risk premium is for long term to boost bond investment.

For instance: Consider a car worth Rs. 1 Crore which is not getting any buyers. Thus the value of asset i.e car is pushed down. The owner can not wait for the financial need. Due to the market conditions, the liquidity risk lowered the value of asset or business.

In maturity risk premium the investor gets the amount to stay back invested for longer duration.