grammar - "The carrots need being chopped" and "The carrots need to chop"

We can say both of the following:

The carrots need to be chopped.

The carrots need chopping.

How does the grammar of these sentences affect their meaning? Why is it that in these instances need takes a passive infinitival clause in (1) but an active gerund-participle clause in (2)?

Relating to this, why is it that we cannot say either of the following instead of the examples above:

*The carrots need to chop.

*The carrots need being chopped.

^{This question is being asked because of this question here, which got migrated to ELL.}

Comments

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