What is the difference between strength training and crossfit?

Metabolic: Strength training is a general term that refers to any form of resistance training whereas crossfit combines gymnastic and traditional exercises typically with high rep/ low rest schemes that will emphasize strength endurance and increased metabolic rate. Classic strength programs use lower rep higher rest periods. There are many types of strength.

They aren't: Mutually exclusive. Strength training is usually a considered a generic term synonymous with resistance training which focuses on muscle contractions against resistance(whether it be your on bodyweight or dumbbells). Crossfit is a sport which involves a series of exercises(often some being strength training exercises) done in rapid succession and high intensity.