This topic is essentially a [[furphy]]. A function and an algorithm are two different descriptions of the same kind of thing. It is a little like saying a spherical box.
An [[algorithm]] is roughly synonymous with a [[method]]. An algorithm / method may return some kind of value to the calling code, but is essentially a block of code used to perform a series of actions or modifications.
To contrast, a [[function]] is something which is required to return a value. It is probably true that there are some programming languages for which this is not a syntactic requirement, but that's the philosophical distinction.
