Texture is a 2D image. There are different processes to create the texture such as math(Called Procedural), a raster image(Commonly referred to as image texture. Technically called a bitmap texture), hard coded(Called coded textures. These are the setting in the shader nodes. Like base color, alpha, roughness, etc of the principle shader), etc.
Shader is the mathematics or the brains of the material and determine what type of mapping is used. Think of a computer. It has difference parts and one of those parts is the CPU. People will refer to the computer using the CPU name. Like I have a Intel computer or I have an AMD computer. Shaders are like the CPU of the material. Just like you can have multiple cores and/or CPUs working together, you can have multiple shaders mixed and added to work together.
Mapping just determines how a texture is applied. For example the “base color” of the principle shader determines what color the surface of the object will be. The roughness of the principle shader determines how glossy/rough the surface of the object will be. Note: both the coded textures are 1 pixel by 1 pixel textures. The base color is a 32 bit color image where the roughness is an 8 bit grey scale image. Side Node: Image Textures that are designed for a specific mapping are referred to by the mapping name. Such as Roughness map, Metalness map, normal map, etc.
Materials are what define how an object looks and it’s options depend on the render engine, but will always contain four elements. A shader, Mappings, Textures, and coordinate system.