After permanent teeth come in, sucking may cause problems with the proper growth of the mouth and alignment of the teeth. It can also cause changes in the roof of the mouth.
Pacifiers can affect the teeth essentially the same ways as sucking fingers and thumbs, but it is often an easier habit to break.
The frequency, intensity and duration of the sucking is a factor that determines whether or not dental problems may result. If children rest their thumbs passively in their mouths, they are less likely to have difficulty than those who vigorously suck their thumbs. Some aggressive thumbsuckers may develop problems with their baby (primary) teeth. (https://www.mouthhealthy.org/en/az-topics/t/thumbsucking)
If your child is still sucking their thumb and their teeth are already coming in, please contact me for a consultation. We can help you avoid costly dental bills in the future.