This is not really much of a computer science question, more a user interface design and/or infosec question.
Are there significantly more computations taking place to check if a password is incorrect than incorrect?
Since there is no third possibility, checking if a password is incorrect and checking if a password is correct, are the same thing. If it is not correct, then it is incorrect, if it is not incorrect, then it is correct.
However, if I mistype it, there is around a 2 second pause.
The user interface design reason for this is to give you time to think about your password. Also, it accounts for the "cat walking across keyboard" case.
The infosec reason is to slow down brute force attacks. A legitimate user who accidentally mistypes their password will only lose 2 seconds re-typing it again. An attacker running a brute force attack who needs to try out trillions of passwords automatically, will be severely slowed down.
The legitimate user will be slowed down from being able to type their passwords about once per second to about once every 3 seconds. The attacker will be slowed down from being able to try thousands of passwords per second to once every 2 seconds.
Typically, the wait time is even made to increase with every wrong try, up to a maximum. Sometimes, there is also a maximum number of wrong tries after which additional measures need to be taken to gain back access to the account, although such a measure is slightly dangerous, since it can easily be abused for a denial of service attack if not designed carefully.