In his most famous essay, "Traditional and the Individual Talent", T. S. Eliot appears to make a distinction between emotions and feelings. Read especially the following passage (emphasis mine):
The experience, you will notice, the elements which enter the presence of the transforming catalyst, are of two kinds: emotions and feelings. The effect of a work of art upon the person who enjoys it is an experience different in kind from any experience not of art. It may be formed out of one emotion, or may be a combination of several; and various feelings, inhering for the writer in particular words or phrases or images, may be added to compose the final result. Or great poetry may be made without the direct use of any emotion whatever: composed out of feelings solely.
However, "emotion" and "feeling" are often used as synonyms. See for example the following definitions from Collins (online):
An emotion is a feeling such as happiness, love, fear, anger, or hatred, which can be caused by the situation that you are in or the people you are with.
Synonyms: feeling, spirit, soul, passion
A feeling is an emotion, such as anger or happiness.
Synonyms: emotion, sentiment.
This does not help one better understand what Eliot exactly means. What is the specific distinction between emotion and feeling that T. S. Eliot is talking about?
NB: I have a similar question about the Preface to Lyrical Ballads where Gareth Rees suggested that in Wordsworth's case, this may be just elegant variation. In Eliot's essay, this does not seem to be the case.