What's the difference between chip away and chip away AT something? [closed]

To chip away, without at, stands for a nearly instantaneous action of (either literally or metaphorically) breaking away a small part of something and thus damaging, or otherwise modifying, that thing. To chip away at something stands for an action that goes on for some time, of trying to damage, or otherwise modify, that thing by (either literally or metaphorically) breaking away a number of small pieces of it.

It should be noted that in the version of the phrase without at, the phrase is followed by a term for the relatively small pieces that are broken away from a larger object, while in the other version, at is followed by a term for the larger object from which the pieces are broken. To use the OP's first example, one can thus say either:

Somebody chipped away little bits of the wood from that step.

or

Somebody chipped away at the step.