No, they are not the same.
Though Chris (in his recipe) refers to allowing the salmon to 'cure' 3 hours he does so because the mix he is using is applied dry and not mixed into water (alone or with other liquids) which would then be called a brine.
'Curing' refers to a process by which the item cured is rendered inhospitable to bacteria. Salt cures meat through osmosis; it draws the water from the meat and dehydrate any bacteria killing them. Mostly, though, meats are cured with a combination of salt, sodium nitrite, possibly sodium nitrate and, often, sugar. Meat must be cured for long term storage and it must be cured if it is to be smoked at low temps, usually between 90-160 degrees. There are curing mixes that are applied dry and mixes that are mixed with water first (a brine) for soaking and/or injecting.
You can apply a dry rub to boneless/skinless turkey breast but caveat: the salt in the mix will draw water out of the meat. If allowed to stay on too long your meat will finish dryer.