The main difference between Highness and Majesty is that the Highness is a style of address and Majesty is a an honorific of Monarchs, usually Kings or Emperors
Highness (abbreviation HH, oral address Your Highness) is a formal style used to address (in second person) or refer to (in third person) certain members of a reigning or formerly reigning dynasty. It is typically used with a possessive adjective: “His Highness”, “Her Highness” (HH), “Their Highnesses”, etc. Although often combined with other adjectives of honour indicating rank, such as “Imperial”, “Royal” or “Serene”, it may be used alone.
Highness is, both literally and figuratively, the quality of being lofty or above. It is used as a term to evoke dignity or honour, and to acknowledge the exalted rank of the person so described.
Majesty (abbreviation HM for Her/ His Majesty, oral address Your Majesty, from the Latin maiestas, meaning greatness) is used as a manner of address by many monarchs, usually Kings or Queens where used, the style outranks the style of (Imperial/Royal) Highness, but is inferior to the style of Imperial Majesty. It has cognates in many other languages, especially Indo-European languages of Europe.
The state of being high.
The quality of being impressive and great.
“the majesty of the Great Pyramids”