Shy cats are not wild cats. They are socialized with people. However, they are not a cat that you can just walk up to and pet.
There are also many 'non-shy' cats that one should not try to do this with as a stranger.
But the difference with a 'shy cat' or 'non-touch cat' is that it is more than just introducing yourself and gently handling it.
A shy cat does not want to be touched in general (yet).
The weakest form of shy cats can technically be touched. If you have built up a bond of trust and are very careful and patient, you can gently pet them a little bit. Typically on the head when you are feeding them.
The most determined shy cats simply cannot be touched, and if they are touched, they will do anything to escape being touched.
That doesn't mean that such a cat can't be social. If the shy cat comes to trust you - which is done by not trying to touch them - it may come and sit next to you. Very close, even.
Like in the seat next to you, at your feet on a footstool. Lie down on the bed with you. – As long as you keep your hands off it.
A shy cat can certainly develop into a 'touch cat'. Certainly the cats that the 'trusted person' can already touch to a limited extent. It can even become a cuddle cat or lap cat.
But whoever wants to give a shy cat a chance (please do that) must do so in the full knowledge that it may remain a shy cat. Forever.
It is (very) difficult to keep your hands off a cat that you feel affection for.
But that is what you should do. Do not impose. The shy cat needs to come to you and allow you to pet it. Enforcing it won't help and will make the cat suspicious and feel unsafe in her home.
NL