First off, I'm going to give you the mainstream view.
"Scythian" was the name the ancients applied to the nomadic Iranian-speaking people living in the area north of the Black and Caspian seas (but often stretching as far west as Bulgaria) from about the 8th to the 1st century BC. Their language was quite certainly Iranian*. There is even one descendant language you can look at today: Ossetian.
There is also a cultural archeological continuity with the Iranian peoples who moved into modern-day Persia and India from this exact area. Here's a nice little animated GIF showing it:
Proto-Turkic does actually have a fairly precise meaning.
The Proto-Turkic language is the linguistic reconstruction of the common ancestor of the Turkic languages. It was spoken by the Proto-Turks before their divergence into the various Turkic peoples Proto-Turkic separated into Oghur (western) and Common Turkic (eastern) branches. One estimate postulates Proto-Turkic to have been spoken 2,500 years ago in East Asia.
One thing should be fairly obvious here: The Scythians lived in West Asia, not East Asia. Also, 2,500 years ago actually post-dates most of Scythian history. These are two almost entirely disjoint sets of people.
So the next question, who is arguing the non-mainstream positions, and why? What I found there is that there are two groups who today argue Scythians were "proto-Turkic": Pan-Turkists and Pan-Turanists. Both of these are political movements, not scientific ones. If either has any good evidence of an ancestral relationship between those two peoples, I was unable to find it in any English-language material.
So what can we say about that history book you read? I guess you have two options. If you are interested in arguing for a larger pan-Asian national identity as a political goal, it's probably great. If you are interested in the mainstream evidence-based view of history, I'd suggest never cracking it open again.
* - As an example, Turkic languages are agglutinative, Indo-European languages are not. It would be next to impossible to misclassify one as the other.