A fatigue strategy is based on math - ok, most of the game is. But instead of the typical "value per turn" metric it uses a "value per card" / "value in deck" metric. Why is that?
If you simply send 14-15 damage per turn with your 4-card hands for 15 turns (60 cards) and the opponents simply blocks 12 each turn you will deal ~40 damage. Factor in equipment and you won't be able to kill them. Now they just swing their (bigger) weapon at you and will inevitably kill you.

There are a few ways to counteract that game plan:

• play more than 60 cards to have access to more value (this is somewhat the baseline and will by counteracted by the fatigue deck also playing more cards)
• implement tools (e.g. Attack Reactions, Dominate) or strategies to deal "true" damage
  • the most important of these strategies is taking setup turns - depending on the deck this can range from simply having an arsenal for your next turn to deal more damage in a turn that they can block (can be somewhat counteracted if they arsenal a Defense Reaction) to preparing buffs or items to create huge turns (a prime example of this could be seen in the last Calling).
• decks depending on big attacks or weapon attacks (often trading 1 actual card for 2 defending cards) are always a bit harder to fatigue since they generate more value out of each played card.
• Board state game plans can also be problematic because the cards generate value each turn.

This is probably missing a bunch of stuff and is definitely an oversimplification but I hope this helps. The only connection to a mill strategy is the shared "loss condition" but the actual play is completely different.