And that incident met the description of an arrest.
You are told you are under arrest.
Wrong. I've been legally "arrested" without ever being told it explicitly. If the officer says you can't leave of your own free will, or attempts to interfere with your efforts to do so, you're under arrest.
You are read your Miranda rights
Not always. Again, I've been "arrested" in the legal sense without getting Miranda'd.
You are searched and handcuffed.
The former of which happened in this case.
You are taken to the station and booked.
Not always.
If this doesn't happen you are not under arrest.
Please don't go into legal practice.
Being detained for awhile is not being under arrest.
Until the cop says you can go...you're legally under arrest.
And there have been cases of "false arrest" that have been prosecuted WRT a cop "detaining" someone without giving them their Miranda warnings or letting them go.
Being stopped for a traffic violation is not being under arrest.
Until the cop says you can go...you're legally under arrest.
Being given a ticket for that violation is not being under arrest.
Finally, you have said something correct. The act of writing a citation is, in itself, not an arrest.