Mist is normally quite a visible, cloud-like weather condition, lighter than a fog, that tends to happen in the cold. Haze tends to happen in the heat, it's less visible than mist and normally due to evaporating water affecting the passage of light. "The valleys were misty, but the hilltops were clear" - you can see mist in the valleys, hazy cannot be used here. "The distant horizon was hazy in the sunshine" - the horizon is slightly blurred, due to water vapour on a sunny day, misty cannot be used here. Hazy can also be used in other contexts: "I didn't sleep well last night and today I feel all hazy" - I can't focus properly.