From Margaret R. Graver's Stoicism and Emotion, on the topic of emotions and feelings:
" . . . [H]aving an emotion is not quite the same as having a feeling. The feeling is our subjective awareness of a physical change in the psychic material; it is something that happens when one has an emotion, but the possibility is left open that it may also occur at other times and for other reasons . . .
This is a point that proves to be crucially important when we seek to understand the norm laid down in Stoic ethics for the optimization of our affective experience. For among the best-attested and most generally known claims of this ethical system is that the genuinely wise person exhibits apatheia or impassivity; that is, the absence of the pathē. Realizing the fullest of human potential means, for Stoics, not only that one becomes able to control or channel the emotions but that one actually ceases to experience emotions as we known them. The distinction between emotions and feelings therefore serves to open up an interpretive space around a central dictum of Stoic ethics. If the psychic sensations we experience in emotion are not simply identical with the pathē, then the norm of apatheia does not have to be cashed out as an injunction against every human feeling. One might be impassive in the Stoic sense and still remain subject to other categories of affective experience.
. . . The capacity to undergo a wide range of feelings is . . . 'hard-wired,' as we would say, into the human psyche. Thus to deny any role for feeling in the life of the wise would be to claim that human beings are endowed by nature with psychic equipment for which we have no legitimate use. As the endowment of nature plays a role in Stoicism analogous to that played by the evolutionary endowment in our own science, this would be the equivalent of saying in a modern context that a creature has evolved capacities which do not promote its effective functioning in its environment. People would have something like a foot in the middle of their foreheads."
Most of this is quite well put, but I feel the analogy with modern evolutionary science runs up against some misconceptions at the end. The misconception is that "evolution" is some magical thing that improves creatures to be better able to deal with their environments. A foot in the forehead is silly, so it couldn't happen. Except that such is exactly how evolution works according to science - random mutations (like a foot in the forehead) that either prove beneficial (and thus evolve into a standard feature), are neutral (and thus survive or fail somewhat randomly), or are maladaptive (and thus cause the extinction of all who share the mutation, thus preventing it from becoming a standard feature). The step that Graver leaves out is that standard Stoicism contains something like "intelligent design" - the idea that the gods, that Nature, is guiding the development of all things. So useless capacity for affective response, like a foot in the forehead, is not possible . . . because the gods or Nature would not allow such a thing to happen.