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Your license and your tag are the same thing. The state doesn't call them tags anymore, it's a license, but there should be months and dates that can be cut out when you harvest your animal. You should have one for bear and one for cougar, if you paid for it.
There is still a "tag" and "license" needed to hunt. Both are purchased as one item. P
You should have tags for both, assuming you paid for the license with both as an option.
You can't check online for licenses purchased because the system is shut down. You would need to go to a license dealer.