The difference between a frost and a freeze is very simple and very complex. The link at the bottom will provide you a very detailed and clear explanation.

A quick explanation: Frost is when a surface loses radiant heat to the level below 32°F even when the air temperature could be higher. An example: We all have seen is our windshields covered in frost in the early morning and the air temperature could be in the mid 30's or higher.   The automobile windshield is colder than the air. Plant also loose radiant heat on leaves and stems causing frost to form. A freeze is when the air temperature is below 32°F for a period of time and the surface areas has lost radiant heat. The cells walls of a plant will began to burst as the fluids expand. When the plant temperature goes back above freezing, the cell membranes release the fluids and water and your plant is now mush. 

Review the attached document from Texas A&M to learn more. Plus, read how best to protection plants from Parker County winters.

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Frost and Freezes