TL;DR. When one makes a distinction between the two terms, which is often not the case, a predictor is an independent variable that is BOTH unconfounded AND associated with the outcome variable, which means that there is a causal relationship between the independent variable and the outcome variable.
In short, the term independent predictor suggests that there is an unconfounded causal relationship between the predictor and the outcome variable. For the record, hormone levels are independent predictors and all independent predictors are independently associated with the outcome variable. The difference between the two terms stems from the fact that independent predictors are unconfounded.
examples:
ice cream consumption and drowning are independently associated, when ice cream consumption increases drownings increase. However, ice cream is not an independent predictor of drownings because they are both affected by a confounding variable, season. In the summer people swim more and eat more ice cream, but its the increase in swimming that leads to increased drowning.
In this case, season and swimming would both be independent predictors. In this case the coming of summer is causally linked to increase swimming rates which is causally linked to drowning. However, there are other predictors that influence drowning that may or may not be influenced by season, such as increased boating or swimming education services.
The TL;DR is that in practice, they are frequently viewed as being interchangeable. However, if you want to be strict and technical, then one could claim that an independent predictor is a variable with an unconfounded association with the outcome variable and thus if you manipulated the independent variable, a predictor would be expected to cause some significant change a non-predictor wouldn't. E.g., swimming is a predictor of drowning, ice cream consumption is not because eliminating swimming would significantly reduce drownings but eliminating ice cream consumption would not have any significant impact even though their natural observed values are associated.
