What is the difference between the different colored dungeon entrances?

Solution 1:

They signify nothing. Dungeons, new zones, and boss battles all show in all colors of light (mostly blue, gold, and white). This appears to be more of a design decision (levels with "cool" color schemes use blue, levels with "warm" color schemes use orange/gold).

^source

Solution 2:

I found this looking for the difference between Gold/Orange doors and Blue doors as they appear on the map. I didn't find the answer here so just in case anyone else stumbles upon this with the same question I had, the difference between the door colors on the map is:

BLUE = Entrance to current area (usually going up). Blue doors go backwards.

GOLD/ORANGE = Doors to the subsequent area (usually going down). Orange doors go onward.