In the meaning "an issue of water from the earth, taking the form, on the surface, of a small stream or standing as a pool or small lake" (from Dictionary), what is the difference between spring and source? Are they interchangeable?
There is a difference in usage.
A spring is the upwelling of water from underground, with a visible flow.
A source is the commencement of a river or stream, it may be a lake or pond with no perceptible inflow.
In more detail: At a spring, you see water visibly issuing from the ground. It may then flow into a pond or may flow away in a stream. The water may be warm, depending upon the depth from which it comes. The rate of flow doesn't matter.
A river's source is simply the point at which it starts. This can be a pond that fills from water flowing down from a hill, the flow into this pond is not necessarily noticeable as a flow.
So, a spring may be the source of a river but a source is not necessarily a spring.