In addition to the distinction between airline miles and hotel points, there's a useful distinction between "miles" and "points" in the airline context alone.

Traditional, miles-based frequent flyer programs (the kind used by United, American, Delta, US, Alaska, etc.) award miles for flights based on distance flown (regardless of fare paid), and generally also set redemption prices according to distance-related geographic zones (no matter what a paid ticket on the same route would cost).

New-style, points-based frequent flyer programs (the kind used by Southwest, JetBlue, and Virgin America, for example) in the United States are generally pegged to the dollar: you earn points for a flight in some direct and fixed proportion to the fare that you paid for that flight, and award tickets are priced in some direct and fixed proportion to the fare of a cash ticket on that same itinerary.