What is the difference between Megalomania and Narcissism?

The lexical approach may assist. The lexical hypothesis states that, ‘All aspects of human personality, which are or have been of importance, interest or utility, have already become recorded in the substance of language’(Cattell, 1943) and, ‘When an idea is important, people are likely to have a word for it … the more important something is, … the more words there are likely to be’(Miller, 1996). The atlas of personality, emotion and behaviour uses a lexical approach to visualise words using the axes of affiliation and dominance (Mobbs, 2020).

Synonyms are:

narcisism: conceit*, egocentricity, egocentrism, egoism*, egomania, egotism, narcism, navel-gazing, pride, self-absorption, self-centeredness, self-concern, self-interest, self-involvement, self-preoccupation, self-regard, selfishness, selfness, solipsism, vanity.

megalomania: conceit*, conceitedness, egotism*, grandioseness, grandiosity, obsessionalism, paranoia, self-importance.

The visualisation according to the atlas approach is shown below:

In answer to your question, there appears to be very little difference between megalomania and narcissism from a lexical perspective.

References

Cattell RB. The description of personality: basic traits resolved into clusters. J Abnorm Soc Psychol. 1943; 38: 476–506. https://doi.org/10.1037/h0054116

Miller GA. The science of words. New York: Scientific American Library; 1996.

Mobbs AED (2020) An atlas of personality, emotion and behaviour. PLoS ONE 15(1): e0227877. https://doi.org/10.1371/journal.pone.0227877

Declared interest: I am the author of the atlas paper.

narcissism is introspective - i.e. an obsession of self/physical appearance. While internalized the disorder personality often seeks out admiration & external merits (eg. Social Media) to affirm the belief.

in context a megalomanic look at ones self as extrinsic from the world: Yet the delusion that they either have the power/ability to influence the rest of the world or the rest of the world is "out to get them" remains absent of influence from external elements.

Distinguishing between similes like this can be aided by a word's etymology. The root of Narcissist is the Greek deity Narkissos, or Narcissus.

"Narcissus, in Greek mythology, the son of the river god Cephissus and the nymph Liriope. He was distinguished for his beauty. According to Ovid's Metamorphoses, Book III, Narcissus's mother was told by the blind seer Tiresias that he would have a long life, provided he never recognized himself. However, his rejection of the love of the nymph Echo or (in an earlier version) of the young man Ameinias drew upon him the vengeance of the gods. He fell in love with his own reflection in the waters of a spring and pined away (or killed himself); the flower that bears his name sprang up where he died." (Britannica.com).

While the word, today, is often used interchangeably with Megalomaniac; a Narcissist is originally speaking to a person who is obsessed with, or overvalues, their appearance. Megalo (big... REAL big - think Megalodon) and mania (obsession) refers to a person's overestimation of who they are compared to everyone else - an obsession with power, influence, or control. Megalomania is a more common combination of a root and suffix, while narcissism derives from the too-pretty-for-his-own-good Narcissus.

Adolf Hitler was more of a megalomaniac; while every artist who sings about how 'hot' they are is a Narcissist (or their lyrics suggest as much at least).

Hope this helps to some extent!

Britannica.com, Narcissus. (2020). Encyclopedia Britannica. Acquired 20 July, 2020 from: https://www.britannica.com/topic/Narcissus-Greek-mythology

Narcissism is an exaggerated sense of self love while megalomania is an exaggerated sense of self worth based on fantasies of power, attractiveness and other physical or psychological attributes and, therfore, all megalomaniacs are narcissists, but not all narcissists are megalomaniacs.

The DSM (Diagnostic and Statistical Manual of Mental Disorders) doesn't distinguish between megalomania and narcissism. The most recent edition of the DSM (DSM-5) classifies both as a form of narcissistic personality disorder.