Textures are pixel based formats and typically 2D. With a wide variety of formats and qualities. The absolute amount of pixel is critical and the real bit depth per channel (not to confuse with per pixel numbers! dpi or ppi are irrelevant)
Shaders are mostly algorithm based functions instead of textures. 2D and 3D versions are available. Most of them are resolution independent! (shader vs texture!)
Materials can contain Textures as well Shaders, and informations to set up an appearance (or result, e.g., light) of an object. These are the only parts that can go into a Material Manager, textures or texture tags nor shaders can’t by itself. (Not in the Object Manager)
Texture-Tags are the container for materials attached to objects, while adding individual information as projections methods. (Attribute Manager). Texture Tags are only available in the Object Manager. Texture tags will be automatically created, if the material is dragged or applied to an object.
.
.
.