I think...
Fe is to do with sympathy. You understand how the other is feeling on a subconscious level. The reasoning behind their emotion does not concern you. E.g: "I really can't imagine what you are feeling, but I know you are feeling bad. Cookies cheer people up. Here, have a cookie."
Fi is to do with empathy. You understand how the other is feeling on a conscious level. You know the reasoning behind their emotion. E.g "You're acting how I would if I were sad or if my dog ran away so I know you are feeling bad. Cookies cheer me up when I am sad. Here, have a cookie."
I think the logic functions can also masquerade as sympathy/empathy.
Eg Ti could reason "I have no idea what feelings are all about but I have the idea that if I give this cookie to you, you will stop crying. Then I can continue thinking in peace."
Or Te "Cookie makes you stop crying. I will give it to you. Then I can carry out my Master Plan. Muhahahahaha!"
Fe is to do with sympathy. You understand how the other is feeling on a subconscious level. The reasoning behind their emotion does not concern you. E.g: "I really can't imagine what you are feeling, but I know you are feeling bad. Cookies cheer people up. Here, have a cookie."
Fi is to do with empathy. You understand how the other is feeling on a conscious level. You know the reasoning behind their emotion. E.g "You're acting how I would if I were sad or if my dog ran away so I know you are feeling bad. Cookies cheer me up when I am sad. Here, have a cookie."
I think the logic functions can also masquerade as sympathy/empathy.
Eg Ti could reason "I have no idea what feelings are all about but I have the idea that if I give this cookie to you, you will stop crying. Then I can continue thinking in peace."
Or Te "Cookie makes you stop crying. I will give it to you. Then I can carry out my Master Plan. Muhahahahaha!"