I would let "direct" mean "linear." The answer then becomes simpler; direct proportional may mean a relationship like 1-1, 2-2, 3-3, etcetera. Proportional by itself would then be free to indicate other proportions; like 1-1, 2-4, 3-9, etcetera -- in an exponential proportion.
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direct means it stays the same while inverse means it will change.
Yes, they do exist. And the question is ...
a is directly proportinal or inversely proportional to b