In engine terminology we use material to mean the asset an artist creates which describes how a surface or volume reacts to light. It will have properties like BaseColor, Roughness, etc.
A shader however is a graphics API resource, not something that artists will interact with at all. Under the hood a material is compiled into multiple shaders to implement the various rendering features, for example there’s one shader that will handle rendering the material in a shadow depth pass. So when you see a message about compiling shaders, that’s the engine creating the graphics API resources needed to implement the rendering features on your materials.