Yes. Some pairs of restriction enzymes will recognize the same sequence and may cut in the same spot, potentially producing an identical cut. These are broadly referred to as isoschizomers.
Other pairs of restriction enzymes can recognize the exact same sequence, but will cut in different locations of the sequence to produce a different set of overhangs. These are called neoschizomers, and are technically a type of isoschizomer.
Depending on the application, having enzymes that recognize the same sequence but cut in a different pattern can be very handy for molecular cloning to generate appropriate overhangs (as opposed to blunt ends).
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