What is a 'Melee Mage'?

I'm personally not a fan of spells cast through weapons, that's not a mage for me, that's just a warrior with magical weaponry.

It does. But the topic is "melee mage" not "warrior with weapon enchants"

My ideas and suggestions are peppered throughout the thread, both in the fantasy and gameplay departments.

This is the ideal battlemage that I wanted in the next DA.

I chose "A Mage that casts spells that focus on close-range" in the poll.

What I mean by a melee mage is an Avatar-style bender or Dr. Strange from the MCU, that also wields small weapons (magically generated or otherwise) to hit things with in close quarters. I typically think of a more rogue-like movement style b/c of magical enhancement to the body like upped speed or agility, or b/c of increased mobility via magic.

The occasional fireball is not out of the question, but it would have decreased range, and might even be changed into a flame burst or touch attack, due to the lack of a staff to focus magic through. Or the fireball's cost would just be increased in comparison to other mages, again due to the lack of traditional staff.