A person who experiences sexual attraction in a way that matches the norm is called allosexual.
A person who never experiences sexual attraction is called asexual.
A person who experiences sexual attraction only in the context of an emotional connection is called demisexual.
A person for whom none of that is true (perhaps they experience sexual attraction very rarely, or in cycles, or only in certain situations) is called grey-asexual.
Another way the difference between allosexual and demisexual people is explained is by dividing sexual attraction into two types. Type 1 sexual attraction is when something external about the person (looks, smell, the way someone moves, their voice, their style, etc) creates sexual attraction for you. Type 2 sexual attraction is when emotional connection creates sexual attraction for you. Allosexuals can experience both. Demisexuals only experience Type 2. Asexuals don't experience either. Grey-asexuals vary. Still a bit confused? this FAQ answers a lot of questions in depth: Under the Ace Umbrella: Demisexuality and Gray-asexuality.
A lot of demisexuals have a time element to their sexual attraction (they need to know the person for a length of time before they can feel sexually attracted), but I don't think this is inherent. I think it just takes a good amount of time for most people to get to a place where they feel emotionally connected. I have spent a good chunk of my life reducing the amount of time it takes me to feel emotionally connected with someone, so I know how to build intimacy really quickly if the other person can be fully present and engaged. So, theoretically, I could feel sexual attraction to someone the same day I met them. This has happened once, when I met someone who was a violet spirit and feminist and trans and cuddly and we went to a cuddle party and talked about meaningful things the whole time. Usually it's not until I've had a 7+ hour conversation on intense topics with the person, and I really doubt it could ever happen in one day with someone who wasn't a violet spirit (violet spirit is a belenen-specific concept that references how I perceive the non-physical aspects of people). I've parsed out the four essential elements for me to feel sexual attraction to someone and I'll make that a separate post.
What about you?