No, they're two totally separate things, and they always have been.
'Constitutional rights' are natural rights acknowledged by the State, while 'civil rights' are rights granted BY the State.
It's why they're referred to as privileges.
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Here's the entire quote:
That these are our grievances which we have thus laid before his majesty, with that freedom of language and sentiment which becomes a free people claiming their rights as derived from the laws of nature, and not as the gift of their chief magistrate.
Thomas Jefferson, Rights of British America, 1774
Sorry - I should have added;
and used to create privileged persons.