I note the distinction, where Fe tends to feel more formal. Note that Fe dominant types are J's by definition, hence it might not feel as free. Usually I feel that some form of specific articulation has to be attached to the connection.
Those who are Fi dominant are P's, so the smiles might seem warmer or more playful. The connection is thus less articulated, more exuded. And they're engaging with their N/S sense, so it's "felt" more than "imposed/articulated."
But I think as people get older and/or more mature, the Fe/Fi thing starts to muddy up a bit. I actually feel like I do Fe more, I can feel warmth but the smile was often a chosen sign. I laugh at my INTP son because we'd just stare at each other sometimes, and then I'd smile at him to show him I cared, and then he'd suddenly smile too as if mirroring me, and then I'd stop and he'd stop... and then we both laughed because we both knew what we were doing.
But that latter laugh? That feels playful and free, more like Fi... something that just resonated inside, not an external symbol, and I responded to it and so did he.
Everyone has all the functions. I think if we learn to recognize the feelings inside and also learn not to try to control the outward expression so much, our warmth can come out spontaneously regardless of type or even considering what "society might think appropriate" or a conscious symbol of our goodwill. In the last few months, I have felt myself warmly engage strangers, spontaneously, without fear, and FEEL it... and felt them respond. It's exhilarating and scary to not be calculating those social connections, and instead to exude them and be vulnerable to whatever comes back.