While I will admit to not fully understanding this ability of yours, here's my interpretation.
Your eyes allow you to see Death, that is to say, a way to introduce the concept of "death" directly into their lifeforce. In order to do that, they also indirectly help you perceive their life to begin with, so as to enable you to strike them at that point.
On the other hand, my magic focuses on taking this lifeforce, and applying it to other means, typically by causing a chain reaction with the "spark" as you called it earlier of the world around us.
Luard sighs and takes a deep breath, briefly coughing into his sleeve before continuing
In other words, both have to deal with life energy, in your case, your eyes use Death as a medium with which to get to life, while mine deals primarily with the life itself.
after taking a deep breath Luard slowly gets up from his position earlier, walking into the office-like room, and gesturing for Shiki to follow
Sorry if this seems a bit short, I've been... More exhausted lately. I believe I shall retire soon, yet for your first day you've made wonderful progress. So much so I'm willing to give you homework. Congratulations.
After glancing around for a moment, Luard opens a drawer.... Only to find more candles. A sigh is heard as he closes that drawer and opens another, this one containing a single, small, paperback book. Its cover is far more intricate than the work itself, and it almost resembles something one might find in a curio shop. Luard takes this book out, and offers it to Shiki
Consider this a handbook of sorts, a guide to the runes I write between the circuits, those that amplify and give shape to a casting. It shouldn't be needed until lesson three, but you may wish to have it to look at for now. Besides, I've already memorized it, so its not like its serving any purpose lying around here.