The contracted forms 's for has and 've for have ...

[WilliamTaft]

"have to" in The Britannica Dictionary:
Usage
Examples of have got are shown above and below for each sense, idiom, and phrasal verb in which it occurs. Note that have got is used only in the present tense. It is common in place of have in informal writing, and it is usual in ordinary speech. The contracted forms 's for has and 've for have are commonly used for the first part of this phrase.
He has it. = He has got it. = (more commonly) He's got it.
......

What's the difference if I phrase the sentence as: The contracted forms 's for has and 've for have are commonly used.?

 

[jutfrank]

I'm not sure what you mean, but if you're asking what 'for the first part of this phrase' means, it's just to be clear that it concerns 'have' and not 'got'.