Many happiness ‘experts’ go out of their way to distinguish between the two, using plenty of New-Age guff and plenty of jargon. They ignore two facts: 1. The distinction isn’t important. 2. Common usage has made the terms interchangeable.
When I refer to anger, sadness, etc. I use the words ‘feeling’ and ’emotion’ interchangeably. So can you.
Yes, there can be a difference: hunger is a feeling, not an emotion. You can feel itchy, but that’s not an emotion. You might be frightened and feel a knot in your stomach – the feeling is the knot, the emotion (fear) is causing the knot. But then again, you can feel fear and feel the knot.
In short, I use the terms interchangeably. You’ll know what I mean.