When do we wish Gemar Hatima Tova , Hatima Tova and Gemar Tov? What are the differences between the three? Does it relate to the High Holiday schedule?
Based on a combo of when I have heard people use these expressions as well as my rabbi's explanation.
Gemar Hatima Tova - is the "full" expression and can be used beginning from the 2nd day of Rosh Hashanna, though, most use it once Rosh Hashannah is over, i.e. beginning the night of 3 Tishrei. It connotes that during Rosh Hashannah one's fate is written and at this point, we wish that the recipient be sealed for good life.
I have not heard the 2nd phrase you mentioned.
G'mar Tov is just a shortcut version of the 1st phrase.
Following this answer of Rabbi David Chai Hacohen the Ashkenazi Jews bless Gemar Hatima Tova while the Sepharadic Jews - Hatima Tova only. The Ashkenazim mean that the Hatima will be good up to its end (maybe Hoshana Raba). Gemar Tov as was mentioned above is a shortage for it.