Well, in English they would be different. "Cada" would be talking about each day and todos will be talking about every day. Cada means you do it like once and todos los literally means all the time. For this, you only make breakfast once a morning (unless you do something different but usually the first meal of the day is breakfast) so "Él hace el desayuno cada mañana" is grammatically correct. If you somehow for whatever reason make breakfast all morning (from 12 am - 11:59 am) it would be "Él hace el desayuno todos la mañana."
Here's a better example, because that may be really confusing: "Tengo que ir al trabajo todos los días, y cada día es un poco peor." I have to go to work every day (todos los dias) and each (cada) day it gets a little worse.
Anyway, I hope this helps. Feel free to reply if you have any other questions.
The speaker combined "hace" and "el" so that it sounds like "hacel". It is relatively common for Spanish speakers to combine words when the first word ends with the same letter that the next word begins, somewhat similar to what English speakers do when they use contractions.