Cite and quote are two English words that have almost the same meaning. Most times, people use to think the two words are synonymous, and therefore, they can be used interchangeably. The fact is, some people are fond of using the number interchangeably but that doesn't mean they are actually the same. Citing simply means to use someone else spoken or written words or findings to validate whatever point you are making.
For example, you might be making a point and you still need more words and points to support your claim, you can easily use other people's words on the same matter to support your claim, but not necessarily exactly as the person said it or wrote it. To quote people means, to copy directly a piece of words that belongs to someone else for your own use. This means you're copying directly with a full sense of acknowledgment towards the person that owns the words. To cite also means to give examples.