Most speakers use them synonymously; some speakers don't:
moreover, beyond what has been said
furthermore, in addition to what has been said
[1] “The acceleration performance of this car model is very poor; furthermore, its fuel consumption is extremely high.”
[2] “The acceleration performance of this car is very poor; moreover, its fuel consumption is extremely high.”
In the first example, the speaker gives 'an impartial, co-equal assessment of the two inadequacies of the car model', whereas in the second example, a critical judgmental sense against the fuel consumption aspect is conveyed. The speaker’s bias shows somewhat.
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