level up vs move up

level up

verb
  • To raise to the same level or status; to improve so as to make as good as others. 

  • To progress to the next level of player character stats and abilities, often by acquiring experience points in role-playing games. 

move up

verb
  • To raise, put onto a higher place. 

  • To move forward (especially when waiting in a queue / line). 

  • To move one's position to allow others to occupy a place. 

  • To be promoted. 

  • To pass to a higher level. 

  • To put higher on a list. 

  • To promote, put onto a higher level. 

  • To reschedule (something) to an earlier date or time. 

How often have the words level up and move up occurred in a corpus of books? (source: Google Ngram Viewer )