I don't know the technical meaning of the two terms, but to me the difference is in how the water is accessed. If the water rises to the surface on its own, I would call it a spring. If a reserve or pool is discovered underground and pumped to the surface by human intervention, I wouldn't call it a spring.
I don't know of any case where thermal waters are tapped without there first being a spring that indicates a geothermal resource there, so all sources I have heard of (in my limited exposure) have been springs.
Thinking about it a little more, the water, when separated from the spring, would be "thermal waters". For example, "Rejkavik provides thermal waters directly to thousands of homes by pumping thermal waters from a distant hot spring into the city's separate hot water system. This water is not potable, but used for heating homes and taking medicinal baths." (This is all imaginary. Iceland has great geothermal resources, but I have no idea if they have such a system. It may or may not exist.)