Hey,
I´m wondering about the same question during my current work. The same difference occurred, when I ran both tools. Did you do a supervised classification? In my case I classified the maximum likelihood. By classifying with this tool,
you include a set of values to one class, while otherwise in zonal statistics the value of all pixels below your mask (shapefile) is estimated. That might cause the visual difference in your result. But I can´t answer the question,
whether a classification or pure zonal statistics is more reliable.
Maybe someone else knows about the purpose and background, both of these tools are applied and interpreted.
Best regards,
Johannes