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The big difference between these two mixtures is the consistency. Sauces such as hot sauces are more liquid than pastes. It is meant to lightly coat food and even enhance the taste of the food instead of covering it up with its taste. Pastes meanwhile are thicker, more viscous, and more concentrated. It’s common to see pastes such as sriracha spread onto food in a light layer instead of being allowed to coat it.  

Chili powders come in at between 500 and 1,500 Scoville units. That's enough to produce a mild burn, but not enough to make really spicy foods.