Difference between FDA and LDA

I have asked this question in Mathematics Stackexchange, thought however that it might be more fit for here:

I am currently taking a Data-Analysis course and I learned about both the terms LDA (Linear Discriminant Analysis) and FDA (Fisher’s Discriminant Analysis). I almost have the feeling that they are used as somewhat of synonyms in some places, which obviously is not true.

Can someone explain me how those approaches are related? Since LDA’s aim is to reduce dimensionality while preserving information from those dimensions and FDA suggests one approach how to achieve this, can I say Fisher’s approach is just somewhat of a subtopic of LDA?

Or as additional question I might add, can FDA and LDA be a synonym, hence be equivalent under any given circumstances?
When would I use LDA, when FDA?

I have already found somewhat of an answer on Wikipedia:

The terms Fisher’s linear discriminant and LDA are often used interchangeably, although Fisher’s original article actually describes a slightly different discriminant, which does not make some of the assumptions of LDA such as normally distributed classes or equal class covariances.

Could someone still go into a bit more detail, please?