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My understanding:

Online Learning: In an online learning setting (for regression problems e.g.), new data becomes available in a sequential order and is used to update the predictor for future data. You don't have a train and testphase, as done by batch learning approaches. It is not defined, "how much" of past data is used to update the predictor.

Incremental Learning: The wikipedia article of online learning makes a difference to Incremental learning:

Online learning algorithms may be prone to catastrophic interference, a problem that can be addressed by incremental learning approaches.

But my understanding is that onlinelearning uses input data continuously to update the predictor, too? Is the only difference, that for OL the amount of previous input data is not defined, whereas incremental learning uses the whole set?

Furthermore, what is the difference of both incremental and online learning approaches in a regressional setting to an expanding window regression approach? Here, a definition for expanding window is according to the pandas documentation:

A common alternative to rolling statistics is to use an expanding window, which yields the value of the statistic with all the data available up to that point in time.

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