This is a good question, Jane :) They are both used only with uncountable nouns. 'Many' more is used with countables, but 'greater cannot be used with them by itself. When using 'greater' to compare uncountable nouns, we must use it with another noun, such as: number, quantity, etc. There is a much greater 'number' of apples on the on the new tree. There are many more apples on the new tree. There is a much greater number of features on the new phone. There are many more features on the new phone. When used with nouns that represent a kind of number or quantity, such as percentage or proportion, they are quite similar. There is a much greater chance of rain in the north. There is much more chance of rain in the north. There is a much greater demand for the second option. There is much more demand for the second option. When used with more abstract nouns (ones that don't really represent a number), again we have to use an extra noun with greater. Such as, level, amount, etc. He showed a much greater level of imagination in the second book. He showed much more imagination in the second book. There was a much greater amount of water in the first lake. There was much more water in the first lake. Essentially, 'more' = 'a greater amount' This is why we don't usually need to include the words 'a' and 'amount' with 'more'. I hope this has helped you, because it wasn't easy trying to explain it :)