Full usually means "completely filled." We often describe a container as 'full': The basket is full of food. We don't say that the food is 'full'.
Plentiful means that there is a lot of it. Saying that there is a lot of food makes sense: Food is plentiful and easy to get.
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It’s perhaps worth pointing out that plentiful is not an everyday word. It’s typically only used in formal contexts to indicate that there’s at least a sufficient amount of a certain commodity, especially an essential one such as food or fuel. The opposite situation could be expressed as a commodity being “in short supply”.