darkneo57, the makers of the Galaxy piano have made a category error, and you are also making the same error.
By category error, I mean that it only makes sense to offer as options things that are in the same category. If someone asks you "is that thing in the corner black or is it a cat?", they are making a category error. It could be both black and a cat, or black and a dog, or gray and a cat, or black and a dog, etc. The question doesn't really make sense.
Stretch is one category. It refers to how far apart two notes that make up an octave are (or double octave, etc). An organ, for instance, generally would not have any stretch. Its intervals are harmonic, making tuning octaves and other big perfect intervals easy; they are simply tuned to whole number frequency ratios (octave A's are tuned at 55 Hz, 110 Hz, 220 Hz, 440 Hz, 880 Hz, etc).
As I said above, all piano tunings are stretched, meaning that the octaves are larger than whole number ratios. If the first note to be tuned is the A above middle C set to 440 Hz, The A below it will be lower than 220 Hz, and the A above it will be higher than 880 Hz. The only question is how much lower or higher, called the amount of stretch, and that is decided by the physics of the piano and to a lesser degree, the taste of the tuner.
Temperament is a different category. It refers to how the octave is divided into 12 steps. If all steps are equally distant from each other, we call that equal temperament. Playing a perfect fifths chromatically (C-G, C#-G#, D-A, etc), all fifths should sound almost exactly the same. Playing major thirds chromatically (C-E, Db-F, D-F#, etc), all of them should sound extremely uniform, though if you listen really carefully, the M3rds will have a subtle beating two octaves above the higher note (at the 5:4 partial coincidence) that will very slightly but uniformly get faster as you ascend chromatically. That's equal temperament.
Other temperaments divide the octave into unequal steps. An early temperament that is very unequal is just intonation. I would not recommend it for general use. In just intonation, the fifths in the primary triads (I, IV, V), are tuned pure (3:2 ratio, more pure than equal temperament), and the thirds in those same chords are tuned pure (which makes them much lower than equal temperament, sounding strange to our "modern" ears), and the remaining notes are tuned to compromises. If you play ascending chromatic P5ths, you will hear that some fifths sound great, others sound absolutely horrible! Likewise, if you play ascending chromatic M3rds, they will all sound very different from their neighbors -- some will be "sweet" while others will sound discordant. If you play a piece in the key in which the temperament was tuned, it will sound very consonant. If you transpose the piece to another key, it may sound very dissonant, or a mix of consonant and dissonant, depending on which other key you choose.
Just intonation is just one of hundreds of unequal temperaments. Most of the other temperaments are somewhere between equal temperament and just intonation, but they all have unequal interval sizes. They are named, often after the person who first wrote about them (Vallotti, Young, Werckmeister, etc). The "later" temperaments, such as those that J. S. Bach may have used, are closer to equal, so there is a different degree of consonance in various keys, but none of them sound horrible, and none of them sound as "sweet" as just intonation.
Your sources are largely correct in saying that in modern Western music, equal temperament is almost always used in tuning pianos. But I know an excellent tuner who tunes a very slightly unequal temperament, and his clients, including some recording studios, are happy with it. By coincidence, I will be tuning an unequal temperament tomorrow for a client who requested it. But it is rare, except in early music period practice performance, "new" music, and world music (where there are many tuning systems that don't really fit into Western temperament ideas).
String quartets and the best choirs (especially straight-tone Renaissance choirs) often adjust their intonation scheme as they perform, and may choose to play important chords closer to just intonation. They might play an E at one pitch in a C major chord, but play an E in an E dominant seventh chord at a slightly different pitch. Since they perform without frets or other devices which fix the pitch of their notes, they can adjust as they go, and it sometimes consumes a lot of their rehearsal time.
So, to sum up, in pianos, first an amount of stretch (for the octaves) is chosen, then the octave is divided into 12 smaller intervals called a temperament. If those 12 notes are spaced equally it's equal temperament. If they are spaced unequally, it is some other temperament, which probably has a name. And the makers of Galaxy pianos are causing confusion by making a category error.