"Masked" refers to the species, while "blue" refers to the color mutation. In other words, they're all the same species. And there are variations of "blue", based on if the birds also possess Dark Factor, Violet, and/or Dilute. Below, right to left, is Blue, Blue plus one Dark Factor, Blue plus one Violet Factor, and Blue plus two Violet Factors. Not pictured is Blue with two Dark Factors, which would be called Slate. And from what I remember, I think a Blue with one Dark Factor and one Violet Factor would also look like the Visual Violet below, except for very minor differences, such as the depth of color on the rump.
The "eye-ring" lovebirds are four closely-related species -- or subspecies, depending on what you read -- that have undergone varying degrees of hybridization in captivity. These are the Masked (
Agapornis personata), Fischer's (
A. fischeri), Black-Cheeked (
A. nigrigenis), and Nyasa (
A. lilianae). The first two are more common in captivity than the last two. What happened is that mutations arose in the Masked and Fischer's (and a rare one or two in the Nyasa), and some breeders crossed them to introduce those mutations into the others.
So, for example, while you might find birds advertised as being mutations of Black-Cheeked lovebirds, they're really hybrids whose mutations derived from Masked or Fischer's lovebirds, and were then bred back with Black-Cheeked for enough generations that they look "close-enough" to pass. Last I remember, there were no confirmed mutations in pure Black-Cheeked lovebirds. And if I remember correctly, the lutino mutation arose in the Nyasa, and was bred into the Fischer's and Masked. Basically, anytime a new mutation arose in the Masked or Fischer's, it was introduced into the others. And this has been going on for decades.
So, at this point, most aren't pure, unless you seek out somebody who maintained pure lines. But what does this mean for you? There's really no need to worry about "keeping them pure" because what you got most likely isn't. The bigger question is what are your goals in breeding them? Are they show-quality? There already are so many parrot breeders out there, cranking out babies that typically don't stay long with the people who buy them.
You're in Texas, so something you could do -- if you want -- is make a large outdoor aviary for these birds and any other eye-ring lovebirds you fancy. There are escaped populations of Peach-Faced lovebirds living and breeding in Texas and Arizona, so unless you're in some cold northern pocket, they'd probably do just fine outside year-round. Fill it with non-toxic plants for cover, maybe enclose a third or a quarter of it for shelter, and you'd be good to go. I'm sure that if you check around you'll easily find other eye-ring lovebirds available for adoption that you could use to build a flock, and just enjoy watching them rather than breeding more.
Just don't mix the eye-ring lovebirds with Peach-Faced in the same aviary. I'm sure some people have done it with no problems, but there has to be a reason this warning was repeated in all my old parrot books. I think the Peach-Faced are just bigger bullies and would wreak havoc on the eye-ringed species if kept together.
So, at this point, most aren't pure, unless you seek out somebody who maintained pure lines. But what does this mean for you? There's really no need to worry about "keeping them pure" because what you got most likely isn't. The bigger question is what are your goals in breeding them? Are they show-quality? There already are so many parrot breeders out there, cranking out babies that typically don't stay long with the people who buy them.