A data field is the smallest subdivision of the stored data that can be accessed. A data field can be used to store numerical information such as price, count or a date or time, or even a data and time. A pair of data fields can be used in combination to hold a geo-spatial coordinate. Also, a data field can be used to hold a block of text. A data field takes up permanent storage within the data-store.
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A variable is a place to store a piece of information. Just as you might store a friend's phone number in your own memory, you can store this information in a computer's memory. Variables are your way of accessing your computer's memory.
