The Chicago police used to (or perhaps still do) take detainees to a site at Homan Square, question them, take them a different police site and then arrest them. Or at least that's what they claim. Can a LEO actually move a detainee miles from the point of initial detainment without arresting them? My intuition says that a LEO moving a detainee that far implicitly puts the detainee under arrest, even if the LEO doesn't make it official until later.
An arrest is the act of detaining a person or property by legal authority or warrant and has been made when a police officer or another individual makes it clear to the person that they are no longer a free person.
A person does not need to be physically touched to be placed under arrest as words alone are capable of bringing about an arrest if they establish that the person is no longer a free person.
Now, if a LEO asks you to accompany them, then, so long as you have the choice not to, you are not under arrest.
This will vary by jurisdiction, but there are clear distinctions between being detained and being arrested.
For example, when you are caught speeding, you are detained but not arrested. You are held locally while the officer processes the citation and attempts to gain evidence for other offenses. You are not free to leave, and despite street lawyers on the internet, asking if you are free to go isn't automatically a get away from police card. Other examples may be questioning a potential suspect near the scene of a crime. The person being questioned is not free to leave, but is not arrested. Note that this type of detention is used overwhelmingly in the USA against minorities ("black man in dark clothing" can apply to whole swaths of society). While specific requirements will vary by jurisdiction, along with what someone who is questioned has to answer, these detentions should be short. If the officer finds probable cause, they may arrest the suspect and take them into custody. The consideration of if there were probably cause or not for arrest can be challenged in court.
Only courts can adjudicate whether police actions fall outside of detention. There is a concept of de facto arrest, which is probably what the Chicago Police actions were. If it looks like arrest (taking someone away against their will and holding them) it probably is.
The general rule is that an individual is under arrest by an LEO when the individual is not free to leave. In criminal procedure jurisprudence this is known as, conveniently, "the free to leave test." Since your hypothetical said the LEO is 'moving' the detainee, I infer the detainee isn't voluntarily accompanying the LEO. So, I'm going to say your intuition is likely correct; an arrest has likely occurred in such a situation.