A feeling is a mental state that requires two things:
- It has to be experienced consciously.
- It has to have a bodily or somatic dimension.
All Emotional experiences are feelings because they are conscious. On the other hand emotions can only be felt through the emotional experiences they create. Unlike feelings, they are not always conscious, and some can be hidden for a long time.
I think that one’s metaphysical and epistemological stance could change how one sees the difference between the two. See dualism.
References
Burton, N. (2014, December 19). What’s the Difference Between a Feeling and an Emotion? | Psychology Today. Psychology Today. https://www.psychologytoday.com/us/blog/hide-and-seek/201412/whats-the-difference-between-feeling-and-emotion
An emotional experience, by virtue of being a conscious experience, is necessarily a feeling, as are physical sensations such as hunger or pain (although not all conscious experiences are also feelings, not, for example, believing or seeing, presumably because they lack a somatic or bodily dimension).