Touch ID or (Enter) Passcode

In Settings of a mobile phone, there is a lable called "Touch ID & Passcode", which is without "Enter".

Source: Google Images.

On the lock screen, there is a sentence "Touch ID or Enter Passcode".

Source: Google Images

More info

Touch ID: from Google Images, Wikipedia and another Wiki. Touch ID is the name of a security feature.

My question

Can the sentence be written as:

Touch ID or Passcode

or

Use Touch ID or Enter Passcode

to keep a parallel structure when the mobile phone is waiting to be unlocked?

Let's imagine you go to the supermarket, and you see a sign that says "Milk", above the refrigerator where the milk is kept. Next to it, you see an advertisement that says "Drink Milk!".

Your question is akin to asking which of these signs is correct. They are both correct and mean different things in different contexts. One is a label, telling you what is there; the other is a suggestion written in the form of an imperative.

Likewise, "Touch ID or Enter Password" is an instruction, in a place where you are required to do one of those things. "Touch ID & Password" is a label for the area where you can find settings related to both of those things. The latter doesn't need the word "enter" because you are not required to enter anything at this point. In fact, because it is not an instruction, it doesn't require a verb at all.

I don't know what your native language is, but I'd be willing to place a low-stakes bet that, if you switched your own phone to your native language, the labels would be the equivalent.