For Eliot, emotion refers to a relatively enduring psychological state, feeling to a relatively transient sense perception. He argues that the act of poetic creation is a catalyst that helps transform both psychological states and sense perceptions into a work of art. He says that great variety is possible in the degree to which any given artwork depicts emotions, feelings, or both. Some artworks focus almost exclusively on emotions, others on feelings. Looking at two examples he cites, from Dante and Keats, can help clarify Eliot's meaning.
Emotions is easy enough. Eliot says of Dante's The Divine Comedy: Inferno, Canto V, that "the episode of Paolo and Francesca employs a definite emotion." The language of the canto makes this quite explicit:
No greater grief than to remember days
Of joy, when mis'ry is at hand!
Or in Allen Mandelbaum's translation:
... There is no greater sorrow
than thinking back upon a happy time
Dante invokes several other emotions by name: for example, the love and lust that Paolo and Francesca felt, or the pity the narrator feels for the sinners. But all these emotions are subsidiary to the very intense central emotion of being tormented by regret.
Feelings doesn't seem quite as straightforward. The difficulty lies in the imprecision with which Eliot uses the term. He says that these feelings may be inhering for the writer in particular words or phrases or images. It is not clear how a feeling can inhere in a word. What Eliot means is that certain words convey certain sense impressions which may not in themselves be connected to larger emotions, but which may still link up associatively with certain states of mind and with other sense impressions. He writes:
The ode of Keats contains a number of feelings which have nothing particular to do with the nightingale, but which the nightingale, partly, perhaps, because of its attractive name, and partly because of its reputation, served to bring together.
The second stanza of Keats's ode illustrates Eliot's point:
O, for a draught of vintage! that hath been
Cool'd a long age in the deep-delved earth,
Tasting of Flora and the country green,
Dance, and Provençal song, and sunburnt mirth!
O for a beaker full of the warm South,
Full of the true, the blushful Hippocrene,
With beaded bubbles winking at the brim,
And purple-stained mouth;
That I might drink, and leave the world unseen,
And with thee fade away into the forest dim:
The image of a glass of wine in turn brings up associated images in the speaker's mind: a cellar, flora, country dance, song, etc. As Eliot pointed out, none of these have anything to do with the nightingale. For the speaker, the glass of wine just feels like the experience of dancing to Provençal song on a green, and in the process of writing, Keats connects such feelings to the nightingale. But these feelings don't by themselves express any specific emotion, such as love, or anger, or despair, that can be pinpointed.
Perhaps associations or sensory images would have been a better term than feelings in this context. However, a close look at the examples Eliot uses to illustrate his conception of poetic creation does make the distinction between emotions and feelings, as he is using those terms, clear enough. It bears mention that for Eliot, the point of the poem is not to express those emotions or feelings. Rather, the creative process is meant to catalyze them into something impersonal, to transform them into an objective work of art.