In the U.S. they're both enabled by the
same clause of the Constitution, so at least in some originalist sense, the intention was similar. It really does come down to the copyright people being more able to secure longer and longer terms. But both predate the U.S. by centuries, so unless interested in the details of American law, we should look to history as well.
Nowadays, copyright and patents are principally governed by a series of international accords and treaties that are implemented and ratified in domestic law by signatory countries. Those allow reciprocity between countries. In the case of the U.S., domestic copyright terms of protection actually exceed the minimum thresholds agreed to under the Berne Convention.
Similar treaties exist for patents. And right now, the term of U.S. (invention) patents is 20 years from date of filing. This used to be 17, but was changed to match other countries' terms.