When you say idle, this means that something is not in use or is not available for a certain period of time. For example, you have left your phone turned on, but you are not using it, this means that the phone is in idle mode. It is functioning, but you are not doing anything to it. Idol is said to be a noun.
This represents someone who may be looked upon by people. There are some people who idolize other people because they feel that some people are living their best lives. These two words may sometimes sound the same, especially when you are not very keen on pronunciation, but they mean different things.
Idle and idol are two different words entirely; they have different meanings, which means there is no relationship between the two words. However, you can easily confuse the two together, especially if you don't listen very well to how they sound. The first syllable of the two words is pronounced in the same way, but the slight difference in their sounds can be noticed if you carefully listen to how their second syllable is pronounced.
Because of their similar nature in sound, you can easily figure out which of the two is being used in a sentence by carefully following the context in which any of the two words are being used. Idle as an adjective is used to describe someone that is lazy, or when someone is inactive. As a verb, it means to spend time doing nothing. Idol, on the other hand, refers to a graven image that is believed to possess spiritual power.