I'm not sure about you, but I've wondered what the difference is between "party sunny" and "partly cloudy"... is this like the glass half full vs half empty? Because I'm all for optimism, but the bottom line is, if I filled the glass and drank half, it's half empty, if the glass was empty and I filled it half way it's half full... I'm sure this is a toilet paper over or under debate...But let's get back to weather.
The National Weather Service definition states that "partly sunny" is when between 3/8ths and 5/8ths of the sky is covered by clouds and "partly cloudy" is when between 3/8ths and 5/8ths of the sky is covered by clouds... so basically "partly cloudy" and "partly sunny" are the same thing. The only difference is that "partly sunny" can only be used during the daytime hours (go figure, huh?).
As you may have guessed, "mostly cloudy" means there are more clouds than sun (or stars and sky, at night). The NWS definition says the sky is classified as "mostly cloudy" when 3/4 to 7/8 of the sky is covered by clouds. "Mostly sunny" is when 1/8th to 2/8ths of the sky is covered by with opaque (not transparent) clouds. This is the same definition as "mostly clear", except "mostly clear" can be used anytime vs "mostly sunny" obviously only during the daylight hours.