Both are hydrocarbon derivatives of petroleum. Natural gas, as the name suggests, comes from underground gas deposits and is ready to use as soon as it’s captured. Propane is a refined distillate based on natural gases from underground. It passes through a refinery prior to being ready to use in your grill.
Practically speaking, both can be used to fuel grills, but they behave differently. Propane burns hotter and drier than natural gas: One unit of propane puts out 2.5 more BTUs when burned than an equal amount of natural gas. For this reason, natural gas–burning grills must be fitted with special manifolds with larger holes to achieve a heat comparable to what you’d get in a propane grill.