should vs wish

should

verb
  • Used to express what the speaker would do in another person's situation, as a means of giving a suggestion or recommendation. 

  • Will be likely to (become or do something); indicates a degree of possibility or probability that the stated thing will happen or be true in the future. 

  • Indicates that something is expected to have happened or to be the case now. 

  • Used to express a conditional outcome. 

  • With verbs such as 'see' or 'hear', usually in the second person, used to point out something remarkable in either a good or bad way. 

  • To make a statement of what ought to be true, as opposed to reality. 

  • Used to impart a tentative, conjectural or polite nuance. 

  • Simple past tense of shall. 

  • In questions, asks what is correct, proper, desirable, etc. 

  • Used to issue an instruction (traditionally seen as carrying less force of authority than alternatives such as 'shall' or 'must'). 

  • Used to give advice or opinion that an action is, or would have been, beneficial or desirable. 

  • Used to form a variant of the present subjunctive, expressing a state or action that is hypothetical, potential, mandated, etc. 

noun
  • Something that ought to be the case as opposed to already being the case. 

wish

verb
  • To bestow (a thought or gesture) towards (someone or something). 

  • To hope (for a particular outcome), even if that outcome is unlikely to occur or cannot occur. 

  • To recommend; to seek confidence or favour on behalf of. 

  • I wish I could go back in time and teach myself what I know now. 

  • To desire; to want. 

  • To request or desire to do an activity. 

noun
  • The thing desired or longed for. 

  • An expression of such a desire, often connected with ideas of magic and supernatural power. 

  • A desire, hope, or longing for something or for something to happen. 

  • A water meadow. 

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