When you first unbox and power on the new Mac, you will see a language selection screen followed by some initial setup steps. One of them asks if you want to transfer information from a Mac or its Time Machine backup. Respond in the affirmative and the setup assistant will begin the transfer. When it finishes, you will be greeted with the same Login screen you have been accustomed to using... just on a new Mac. All your apps, accounts, documents, etc will be identical or upgraded versions of the same ones (in the case of macOS native apps).
It really does not matter whether you choose the Mac or its Time Machine backup as the source — provided of course that TM backup is the most recently created one.
... just need to know if the two machines having different OS will cause any issues...?
It is the normal and expected way of replacing a Mac with a newer one. It's how Apple designs it to work, and how I have been doing things since 1995 or so.