I have just bought an Electric Generator / Electricity generator. It works very well.
Sometimes, I'm confused when using a noun with adjective or two nouns together. Please help me to distinguish them clearly
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Normally in English only proper nouns (names) are capitalised. In normal text it would be written:
electric generator / electricity generator
So in my view, neither are correct.
However, if you are asking about choosing electric versus electricity then the second is a better description. It generates electricity; it is an electricity generator. However often such words are contracted and it is often found more convenient to write electric generator, which is symmetric with electric motor. An electric motor uses electricity and cannot be called an electricity motor! The ambiguity only exists on your example (with a generator).
Other words that we might find used with electricity are:
electricity meter, electricity company, electricity bill, electricity plant
These all relate to the supply of electricity, but all may often be shortened to electric.