First of all let me say what my gender therapist told me a few years ago.: (I am a post-op trans woman)
"I am sexually attracted to males and romantically to females."
Although I am still a bit confused with my orientation, which I don't see as a problem. I don't consider myself bi-sexual, more hetero flexible.
Asexual has come to my mind a couple of times, as I am not really interested in actual physical contact with man or woman, but fantasize about it when I masturbate. I am very much in love with my XXXL toys and anal play by myself. I certainly am not into relationships and drama, at the most a one nightstand or friend with benefit. So to me the difference is fantasize vs reality. In the last 2 years I only had 1 encounter with a male, just a blowjob. No intercourse or anything else.
What I like with woman is actually like you mentioned, go out in public have dinner etc, cuddle, kiss, go oral downtown, perhaps masturbate each other. Orgasms is not mandatory.
With man I dream of getting rough sex, penetrated and oral. Being for his pleasure No orgasm for me needed.
But like I mentioned, I have hardly any experience. Before I transitioned I thought I was gay/bi and had sex with both man and woman, much more man though. As far as sex with woman, including my wife, 5 in my 56 year life time, with man its uncountable, but 50% told me I was acting like a woman when we had sex.
So yes, I am not sure if I might be asexual. Good question.