Difference between ''moreover'' and ''furthermore''

Question

What is the difference between the words ‘‘moreover’’ and ‘‘furthermore’’?

The exemplary sentences on Merriam-Webster are

‘‘Swimming alone is against the rules and, moreover, it's dangerous.’’

and

‘‘She always arrives on time; furthermore, her work is always excellent.’’

The difference between these two sentences is that in the first one, we add information that is used to emphasize the argument of the first part of the sentence. Whereas in the second sentence, we only add information, which is not necessarily directly connected to the information given in the first part of the sentence.

Is this the difference between ‘‘moreover’’ and ‘‘furthermore’’? Or can I use them interchangeably?

Answer 1

Here's an interesting old explanation I've found (just removed some obsoletely used commas and added emphasis where it seemed useful):

The difference between words, esteemed synonymous... (p. 73 Trusler, John, 1735-1820)

58. Furthermore, Moreover, Besides.

Furthermore is properly used when there is need only to add one more reason to those before-mentioned; its intent is to multiply and it has no relation but to number.

Moreover is in its right place when used to add a reason of a different kind to those that went before; its chief office is to add, with a particular respect, to diversity.

Besides is used with propriety when we would strengthen by a new reason the force of those that were sufficient of themselves; its principal office is to enhance by abundance.

[examples:]

For a state to support itself, those who govern should be moderate; those who ought to obey, governable; furthermore, the laws should be judicious. There will always be war among men, because they are naturally ambitious and are governed by interest; moreover, zeal for religion makes them rigid. Holy Scripture teaches us the unity of the Godhead and reason points it out to us: besides, all nature makes us perceive it.

https://quod.lib.umich.edu/e/ecco/004892937.0001.001/1:7.58?rgn=div2;view=fulltext