Liquidity versus Illiquidity

Here is a paraphrased email I received concerning the terms Liquidity Premium and Illiquidity Premium which may be helpful to clear up some confusion:

After reading over and over the source reading and online references, I finally came up to understand that Liquidity Premium and Illiquidity Premium is interchangeable (they both are the same, just with different names). But that liquidity and illiquidity are NOT interchangeable. Liquidity really means something liquid, while illiquidity means something not liquid. And the difference between the IFRS 17 discount rate and the risk-free rate is the LP or IP (it seems like in Canada and UK they use LP while other countries use IP).

It makes more sense to use the term Illiquidity Premium, since the higher the LP or IP, the higher the illiquidity. and low LP or IP mean higher liquidity. I just think that using Illiquidity Premium makes more sense to understand the concepts, since it is correlated with illiquidity. And since CIA says that both can be used.