We experience life at a very high level of abstraction, working at the symbolic rather than functional level. When we perceive a sunset, there are loads of external symbols that are recalled to varying degrees, depending on the individual and the associations built up around the symbol ‘sunset’. These associations may make the sunset more ‘spiritual’ or ‘magical’, but to cut through the excess baggage and clarify the concept ‘sunset’ as a strictly physical phenomenon is the goal of the reductionist.
Similarly, the concept ‘value’ is entangled within so many associations that are built up within the years, that it has become nearly worthless for communicating ideas. You provide the definition “to - at this moment - consciously perceive X as conducive to my happiness”. I do not dispute this definition. Perhaps initially our great ancestors had no concept as value except in the way you define it, but over the years, as similar objects were valued for similar reasons (water, shelter, group of people for cooperation), the concept developed an amount of conceptual baggage such that it became ‘any object or quality desirable as a means or as an end in itself’.
We can see the above in action with gold, and how many hard money cranks (distinguishing from mere hard money proponents, who like it for its stable supply) have, because it was historically valued as a means of exchange, began to see it as valuable in and of itself.
Notice how value as verb is reducible to individual preference. Value as noun, however, is not. The associations built up and eventually overshadowed the original meaning of the word, so that discussion re: value has became complicated and frustrating for all involved.
On to your question. By ‘similar in kind’ I mean that, because all statements of value are reducible to preference, from valuing a laptop and not wanting it to break to valuing human life and not wanting it to expire, then our physical and emotional responses are (unless I’m mistaken, but I don’t believe so) similar responses. The difference being that most people’s preferences regarding typical moral concerns (life, kindness, liberty, incest) are embedded to a higher degree within their worldview, and so the ‘moral sentiment’ is usually of a correspondingly greater degree.
I would not be too confident in personal experience of moral sentiment and proclaiming ‘ah! I can differentiate the two’. It is difficult to separate our actual response from the associations that we have developed around the object of our sentiment. In my own introspection, I cannot differentiate on feeling alone between the discomfort of failing a class or losing something highly valued and that of moral discomfort. It is only when I turn to the object of my sentiment that I can differentiate it as moral or not.