Infectious disease doctor and pediatric infectious disease do the same thing?

Yes: An infectious disease doctor usually treats only adults and adolescents. However, they may have training for pediatric cases as well. A pediatric infectious disease doctor specifically treats kids. Just ask the infectious disease doctor whether they have training in pediatrics if the patient is a child.

Not exactly: All infectious disease specialists treat all things infectious as the result of bacterial, fungal, vital, or parasitic infection. They may treat children at some point but they also deal with adults. Pediatric infectious disease on the other hand is a sub-specialty of this group that treats only children and the infections specific to this population.