Does Touch ID work differently between Apple Pay and iPhone unlock?
No. You may experience slower response times due to presence of moisture or dust on or under Touch ID sensor or finger/thumb respectively.

Cleaning/Drying the Touch ID sensor/finger usually resolves the lag issue.

iPhone 6s and later (excluding iPhone SE and all Touch ID equipped models of iPad) have a second generation Touch ID sensor which is much faster at recognizing finger/thumb geometry.