Alternate visuals when catching
Solution 1:
The animation with fiery wisps going up is the critical catch animation. In this case, the Ball will have shaken only once. A critical catch increases the chances of catching a Pokemon substantially, but has no other effect.
The ring going out with 3 stars flying outwards is the normal catch animation. In this case, the Ball will have shaken three times.
Any other animations, including the Ball only shaking once without the wisps or no animation at all (just the "Great!"), are visual errors caused by connectivity issues.