According to Howard Gardner there is intrapersonal and interpersonal intelligences.
You differentiate between intelligence and skill. How do you define the difference? I would say that skill has less of an inherent quality being mostly learned. Emotional intelligence, like verbal intelligence, can be learned to an extent but has an inherent quality as well.
Describe your definitions for intelligence.
If something is - in essence - an aspect of the same thing, you'd expect high correlation between both. There isn't such a high correlation between 'Intelligence" as defined by the G construct and "Emotional Intelligence". Therefore emotional intelligence is not 'intelligence' as defined by G. However things like memory, processing speed, size and duration of neural activation patterns, spatial rotation, vocabulary and a plethora of other cognitive traits traits ARE highly correlated with each other. Emotional intelligence just doesn't fit in that framework. Because it's not intelligence. It's a talent, or a propensity for the interpersonal there are already perfectly good terms for that.
From the about hundred of years of research on the topic it seems like traits related to intelligence are more wholistic. ie: someone who is more intelligent than someone else will generally be better at about every type of cognitive task, it's not the case for something like 'emotional intelligence' which is much narrower. Hence it's proper classification as a 'talent' / propensity etc.
Furthermore intelligence doesn't vary much if at all throughout life. Emotional Intelligence is in large part a function of preference and experience. ie: someone more emotional or more social who will then LEARN to read people. You can't learn yourself into being smarter, wiser yes, not smarter. Yet you can 'learn' to have a higher "EQ" - again because it's not a form of intelligence.
The popular perception of intelligence as 'narrow' is what makes "EQ" an attractive concept. But it's just that, a popular belief. A 140 iq individual has a brain that - overall - quantitatively and qualitatively outdoes an iq 100 individual at nearly everything. That is hard for people to accept, hence the attractiveness of oversimplification of what intelligence is that's been popularized by the have nots in that particular area.
Enough said.