Here's a long reply, so take a break first, sit down with a drink and a snack, and read on!
There were a continuing series of color tube improvements over the years, involving not only phosphors but also the tube construction. Of course, when a big advantage was obtained by one company, others had to adopt it to stay competitive in that wall of TVs at the appliance store.
In the very first phosphors used experimentally, the red was so poor that a color filter was needed over the faceplate. By the time NTSC was adopted, this wasn't needed, but the red still needed about twice the drive of the green or blue. The green at that time was a willemite P1 green, more a pure green than used presently, and having a rather longish decay.
One early change was to go to all zinc-sulphide phosphors. The green became more yellow, and also had a shorter persistence, matching the other colors more closely in this regard. The red was somewhat more efficient, I believe, but nowhere near the later rare-earth reds.
The introduction of rare-earth red phosphors was a major revolution in brightness. ( I'm not sure off the top of my head, but I think Sylvania was first.) Now the current ratios fo the three guns was more nearly equal, and, depending on the white set-up color, the green might need a bit more current than the red. Also, it was discovered that adding cadmium to the green sulfide phosphor increased its efficiency, at the expense of making it even more yellow. This moved the cyan edge of the color triangle towards white, so really saturated cyan colors could not be produced. The Newport cigarette pack is an example of a color that is in the original NTSC gamut, but outside the range of modern phosphors (but cigarettes can't be advertised on TV now, anyway!). Cadmium was dropped eventually, because of problems of handling this toxic element, so tubes went back to the plain sulfide green, which gives a good gamut of colors, not quite as wide as the original NTSC.
Zenith introduced the black-matrix "negative guardband" tube. Black matirix means the phosphor dots are surrounded by black material to reduce screen reflectance. Negative guardband means that the phosphor dots are smaller than the holes in the shadow mask. Since the dots might vary in light ouptput over their surface, you could get color errors in old the positive guardband case when magnetic fields would make the electrons land on different parts of the phosphor dot, so purity adjustment was more critical. Essentially, the negative guardband tube allowed higher beam power for more brightness, since shadow mask expansion could go further before causing a problem. RCA, I believe, introduced invar shadow masks in some tubes, also as a measure to reduce effects of mask heating. The ultimate in this regard was the tension mask, which does not undergo any distortion until it becomes hot enough to relieve the pre-tensioning and sag.
Sylvania, if I remember correctly, had good results with changing the physical processing of the phosphors, adjusting the particle size and the thickness of the slurry used to deposit them. The thicker slurry required extra care to prevent swirl marks due to uneven application.
Sony's Trinitron introduced the tensioned shadow grill, which was more transparent to the electron beams and increased brightness (but lost contrast because the ratio of black matrix to phosphor area decreased). It also had an improved electron gun that could produce a better spot size at high currents. Better electron guns for the shadow mask tube were also developed, and the shadow mask tubes went to in-line guns and striped phosphors. The use of in-line guns made the vertical deflection of the electrons irrelevant to purity adjustments (if the beam moves vertically, it just stays on the same color stripe). This new degree of freedom allowed the development of self-converging deflection systems that needed no circuitry or adjustment once the yoke positon was set at the factory. This was a major breakthrough in reducing the cost of color TVs.
Projection TV introduced new problems, since the sulfide phosphors (blue and green) tend to saturate and produce sub-linear output at high current densities (highlights go pink). this was solved in varioius ways by using non-linear circuits (mainly in the blue) or new phosphor formulations (mainly in the green).
The changes in phosphor color over the years, in order to obtain improved brightness, had effects on the color reproduction. It is possible to correct exactly for a change of phosphor primary colors, but this has to be done at the camera before the signals are "gamma-corrected" to match the non-linear electrical characteristics of the picture tube electron gun. When PAL was standardized, they settled on current phosphors (including the non-cadmium sulfide green). NTSC, however, has been operated under the FCC dictum that the encoding is "suitable for" the original NTSC phosphors. Therefore, receiver designers have put adjustments in the color decoder. The problem is that since sulfide green is too yellow, it's like getting some red you didn't want in every mixture of red and green, including fleshtones. So, you have to increase the R-Y color-difference gain, so when it goes negative (reduces red and increases green), you really reduce red a bit more. That means that when you increase red, you also increase it more than you would before. If everything were linear, this would be just right to correct the reproduced color. However, because of the non-linear characteristic of the electron gun, the turn-on gets enmphasized more than the turn-off, resulting in overly bright reds, while flesh tones and less saturated colors are correct. This situation has finally been corrected in the new HDTV standards, which have settled on a set of primary colors very similar to the PAL colors. These primary colors have also been carried over into digital cameras (and computers to some extent) as the "sRGB" standard.
By the way, although the green phosphor color has changed the most from the original NTSC, the blue has changed also, toward violet. This is sufficient to change fleshtones slightly greenish, since the yellow obtained from mixing red and green must be complementary to the blue phosphor. This change is also standardized in PAL and HDTV. The red has also wandered a bit toward orange and back, but it is still close to where it started. (By the way, traffic-signal red has always been outside the range of reproducible colors.)
The change in white color over the years is also worth mentioning. The NTSC settled on Illuminant C, an approximation to the light from an overcast day. (The modern equivalent is D65.) Nearly all sets from the earliest 21-inch RCAs onward, however, went to 9300 degrees Kelvin, which is quite blue. (Some had another preferred setting, but it typically wasn't Illuminant C.) This was partially a result of matching the black and white sets that people had gotten used to, partially to make the whites look "whiter", perhaps partially because 9300K is what you could get with reasonable current ratios for the three guns, and perhaps because the reds, yellows, etc really look brightly saturated when compared to a bluish white. The drawback is that color errors in fleshtones are exaggerated. One thing that drives videophiles crazy today is that some manufacturers still set the white point quite blue.
All the above applies to CRTs. Plasma screens use different types of phosphors that respond better to the UV discharge, and may have somewhat different primary colors. The first ones had much oranger red than CRTs. LCDs and micromirror (DLP) devices depend on the spectrum of the light source combined with color filters.