Average rate is the rate stored in channel state. While sats are spent on LN their amount in channel variates with regard to real LN invoices. However, the channel liquidity is denominated in some other assets so with every spend average rate (in sats) adjusts reflecting the amount in sats spent and the price in sats at this moment.

Server rate is present rate observed by server (DLC oracle in future). That's for information and transparency.