Describe the difference between competency to commit a crime and competency to stand trial?

This question is essentially asking the difference between
capacity to commit a crime and competence to stand trial.  There is a link to each
below.

The capacity of a person to commit a crime has to do
with their mental state at the time that the alleged crime was committed.  They must be
able to understand what they are doing -- the nature and possible consequences of their
action.  By contrast, competence to stand trial has to do with the person's ability to
comprehend the charges against them and participate in their own defense at the
trial.

For example, a person may be percectly competent to
stand trial but may plead not guilty by reason of diminished capacity to a first degree
murder charge.  They may say they were drunk when they committed the crime and could not
have formed the intent necessary to be guilty of first degree murder.  Now that they are
no longer drunk, they are competent to stand trial.  In this case, the difference
between competence and capacity would be a crucial one.