The traditional western elemental correspondences are as such;
Earth: Relates to the North, the new moon, winter, the color green, life cycles, and midnight. It has power in grounding and that translates into the realms of protection, money, hearth, home, etc. In Tarot and various Pagan paths the element is represented by Pentacles.
Air: Relates to the East, the waning moon, spring, the color yellow, and sunrise. It has power in communication, moving through unseen realms of thought, wisdom, intellect, etc. In Tarot and various Pagan paths the element is represented by Swords while others Wands.
Fire: Relates to the South, the full moon, summer, the color red, and noon. It has power in heat, purification, destruction, passion, creativity, etc. In the Tarot and various Pagan paths the element is represented by Wands while others Swords.
Water: Relates to the West, the waxing moon, autumn, the color blue, and sunset. It has power in emotion, intuition, change, adapting, blessings, overcoming obstacles, etc. In the Tarot and various Pagan paths the element is represented by cups.
The Fifth Element: There are some more modern Pagan traditions that use and recognize a 5th element, the element of Spirit. This is also known as akasha or aether and is the bridge between the spiritual and the physical - part of the universal energy.
All of the information regarding the elements, their Correspondences, and their uses in Alchemy makes sense to me and working with them has never been a problem. So, I have never really felt like I needed to explore the subject at different angles, look through the information with different lenses, or meditate deeply on the elements and their connections.
It was not until coming across the Blacktree tradition that made me sit back and do a double take regarding the elements and their Correspondences. The Blacktree's interpretation (which was originally put forth by Robert Cochrane and is called The Northern Quarter System which is based out of the four winds of Celtic Tradition) is thus:
Earth: This is placed in the South becuase the Earth dwells beneath our feet.
Air: This is placed in the North becuase air is above us.
Fire: This is placed in the East becuase the sun rises there.
Water: This is placed in the west because water can always be found in the west. In addition, it is where the sun sets and is the home of the West Gate, where the dead are said to enter the underworld (Hel).
The elements, their powers, and other associations do not change or differ much other ways.
These correspondences also align with the four qualities given to them by the philosopher Aristotle - hot, cold, dry, and wet.
The Northern Quarter System is a more land based way of looking/interacting with the worlds and how the spiritual interacts with the physical and vice versa.
This system also gives us a variation on the traditional pentagram. It stays compass like and there is no discernible way to say there is a right side up or what have you. It also creates a need for different technique when using it to invoke or banish per the techniques put forth by The Golden Dawn in their Lesser Banishing Ritual and others. When invoking the person starts at the point of the element that is being used and traces clockwise and for banishing trace counter clockwise.