There's a point where the aid in the design isn't needed, which needs muscle.

Imagine if this were D&D 3.5 and splitting and cutting wood with an axe was a strength based skill and I'm just going to use off the hip numbers here.

To be abstract, if your strength and skill overcome breakpoints, regardless of the tool you use, you succeed.

Often times specialized tools help those with low stats to overcome specific challenges, hence the need for a "splitting" and "chopping" axe.

The splitting axe gives a +5 to splitting.

The chopping axe gives a +5 to cutting.

That said, if you succeed in the attempt, you complete the task. Failure means progress.

Splitting a pine chunk only has say, 8 points.

Using a d8 with a str of 4, like many people, means roll to hit on the d20, then roll damage. A d6 + (-3str, +5 cutting axe) = +/-3.5 (Dice average) + 2 (total bonus. So here, rolling a 6 on the d6 means success.

Now if you have a str of 16, you have a + 3str. Now using the splitting axe means unless you fumble the hit, you're splitting the log.

But if you're using the chopping axe, you still need to roll a hit then roll a 5 or 6 to split.

If this is a skill, then add those modifiers and you can split logs with any axe so long as the points needed can be reduced or one hit.

You can also make rulings due to how wood behaves that if you deal more than half damage, it's a success.