Demigreysexual is a sexual orientation on the asexual spectrum defined as someone who is demi- and greysexual.
Demisexual is a sexual orientation on the asexual spectrum defined as someone who does not experience sexual attraction until they have formed a deep emotional connection with someone. The connection can be romantic, platonic, or some other form of connection. What counts as a "close connection" can vary between demisexuals. Forming an emotional bond with someone does not mean that one is automatically attracted to said person, as it just means there's now a possibility for one to feel attraction.
Greysexual or Greyasexual, also spelled Graysexual or Grayasexual (shortened to Grey Ace or Grace) is a sexual orientation on the asexual spectrum, referring to those who relate to asexuality, yet feel that there are parts of their experience that aren't fully described by the word asexual. Greysexual can be used as a specific identity, or as an umbrella term for any ace-spec identity that isn't purely asexual, including demisexual and others.
A common reason someone may identify as greysexual is that they experience sexual attraction but very infrequently. Some greysexual people may only feel sexual attraction once or twice in their life. Others may experience it more frequently, but still not as frequently as allosexual people.