Since my 10000K 70W MH lamp have rare-earths instead of indium, I plans to buy a higher kelvin 70W MH lamp from Aliexpress. However I'm fearing of buying a MH lamp that it is pure blue, as its light may be worse as white and blue LEDs in terms of health and comfort.
I found this video where a US aquarium lighting admirer bought a Plusrite 175W 20000K probe-start MH lamp for his aquarium, and he describes the 20000K color as pure blue (Like blue colored indium iodide lamps for colorwashing), and the video also show this.
Is blue and 20000K in a MH lamp the same color? Or is it slightly whiter than pure blue?

There is no single "blue" color, nor any single "20000K" color.
So yes, 2000K look bluish, but "normally" stating the CCT implies it should contain all color components (even though the red and green are weaker than blue).

Regarding the physiological effects, it would be the same as any other light containing significant part in blue: It will make your body to "think" it is a midday and so mess up with your "biological clock" when used at night (and fix it when used during the daytime when e.g. working out of the natural daylight reach)

So how the amber color of LPS lamps considered as 1700K, despite it is monochromatic (Even more than an amber LED)?

So how the amber color of LPS lamps considered as 1700K, despite it is monochromatic (Even more than an amber LED)?

No. The color is stated as the wavelength of light in that case (e.g., 589 nm for LPS).

But in James Hooker's website, the CCT of LPS lamps is stated as 1700K.

But in James Hooker's website, the CCT of LPS lamps is stated as 1700K.

I’ve seen that too. It’s the closest color temperature to 589 nm light. If you wanted to, you could use 20000K to describe pure blue. Hope that clears things up for you. 

So how the amber color of LPS lamps considered as 1700K, despite it is monochromatic (Even more than an amber LED)?

Each black body temperature represents its spectrum. The "Correlated color temperature" is then obtained as the temperature of black body radiation with the highest correlation between the "tested" spectrum and the spectrum of a black body radiator at that temperature get the highest correlation product.
So even when the LPS is monochromatic, it yields some correlation product number with any other spectra, different with different ones. As the CCT parameter takes only those spectra emitted by a black body, spectrum of each compared temperature gives its corresponding correlation result. The temperature of the black body yielding the highest correlation is then defined as the CCT. So for the monochromatic LPS the highest correlation is obtained with the spectrum of a 1700K black body, hence the CCT=1700K.

The correlation is a mathematic operation between two functions
Correlation(func1, func2) = integrate(func1(x)*func2(x)*dx, for x within the definition range)
yielding a single number, telling how similar those functions are. It could be positive (very similar or identical functions), small number (dissimilar functions), zero (ortogonal functions), even negative (functions of opposite polarity values). Here those functions under question are power density as function of wavelength. Per definition the power density can be only positive, so the correlation can never be negative.
So when calculating correlation between two monochromatic lights, you get zero. When correlating any visible wavelength with a continuum over the whole visible range, you always get some nonzero value. And depend on the shape of the continuum spectrum, the correlation then could be higher (that wavelength is in the part where the continual spectrum has higher density) or lower (when the continual spectrum has lower density at the wavelength of the tested source). Of course the "reference" spectra of the black body radiator are normalized, so the correlation results could be compared.
The CCT then defines the wavelenght definition range to calculate the correlation as the "visible wavelength range", so the IR radiation of the black body is not taken into account.

There's a chart on this article that explains it more visually. But no, blue and 20,000K aren't the same, and neither are blue and infinite kelvin.

https://en.wikipedia.org/wiki/Planckian_locus

There's a chart on this article that explains it more visually. But no, blue and 20,000K aren't the same, and neither are blue and infinite kelvin.

https://en.wikipedia.org/wiki/Planckian_locus

The very high CCT (20k+ K) is of a tint many just call "blue". Of course not a saturated blue, but just a blue.