Sense: touch, seeing, smell and so on. One could argue what all senses are, but this is the characterization of it.

Emotion: a process that involves cognitive interpretations of your context (environment + thoughts) and a physiological feeling through the senses (heart rate, tingly sensations, weird feelings in eyes). Check out the James Lange theory. There are better theories, but this has the fundamentals.

I ad libbed this one, I wanted to show that there is a difference. It wasn't my intention to be pinpoint accurate.