Some of the typos in the question:
“is consider” -> “is considered”
“track in lament term” -> “in layman’s terms”
“there are music” -> “there is music”

I would agree with you. A new piece of music that uses samples is not a remix unless it is substantially like the original.

In some cases, a new composition is clearly a remix, or is clearly something very different.

In some cases, it may be questionable, and for any line or definition someone would try to establish, it would be possible for someone to make a piece that sits on that line and makes it hard to categorize that way.

A remix would have content from the original track. Parts of it or even the entire track. As long as musicians are adding newer elements to the original track, it is considered a remix. For example, we have the swing music from 1920s. The modern version of it is called Electro swing. Most of the remixed versions have the original tracks intact, with added layers of electronic music and beats. They even change the tempo of the song but the basic old track is the same.

@Zaku I am never one for grammar.

Edit: I just realised mashup is also considered remix to me, so Building Steam in A Grain of Salt is consider a mashup/remix