You can’t make a texture emissive or diffuse, you can plug a texture to emissive or diffuse (Base Color in UE4) parameters of material.
If you set a material as unlit, you will only have Emissive and World Position Offset sockets available. I guess reasoning behind it is that if a material is not iluminated by light (Unlit), only way that it can seen is if it emits light, thus why Emissive is only available. Also, Base, Metallic and others are all used to calculate final result taking into account light received by object. If material is not affected by light (that’s meaning of unlit), they are useless.
Here you have a screenshot for completeness.
