Natural crime is not a term with which I am familiar, but I am going
to assume that it is a term related to an important concept in
philosophy/theology: natural law, which might be defined as St Paul
did as laws that are written in the hearts of humankind by God. For a
full discussion of this I refer you to:
"Founded in our nature and revealed to us by our reason, the moral law
is known to us in the measure that reason brings a knowledge of it
home to our understanding. The question arises: How far can man be
ignorant of the natural law, which, as St. Paul says, is written in
the human heart (Romans 2:14)? The general teaching of theologians is
that the supreme and primary principles are necessarily known to every
one having the actual use of reason."
This same webpage cites "honor thy parents" and "do not commit
adultery" as instances of natural laws that "No person whose reason
and moral nature is ever so little developed can remain in ignorance
of...except through his own fault."
Legal crime, on the other hand, is an act that violates a human-made
law, contained in a legal code. Legal codes, at least in most
countries, do not impose penalties for committing adultery or for
showing no respect to parents. Though legal codes may not embody all
the precepts of natural law, they must not--if they are to be obeyed
by those who believe in a higher or natural law--condone conduct that
is contrary to higher law. Martin Luther King's civil disobedience,
for example, was aimed at unjust laws that violated natural law.
For him, the "legal crime" was not a crime at all because the law that
defined it as such was itself unjust: a crime against "natural law."