If you notice the male loiselli has green on his sides and the male freddy is more solid yellow. They do look completly different in person. Much more so than in the pics where they look really similar. The loiselli male has green and blue around the vertical bars. This is absent on the freddy.
When I first got the "freddy", he had a bunch of purple up top. I found a picture online of a freddy that looked exactly the same. But since he's settled in, the purple doesn't show much. The body shape between the two is also slightly different although I'm not sure this neccessarily means they are different. The loiselli is more football shaped and higher bodied while the freddy is more streamlined.
Here's a couple of pictures to better explain.
My male freddy the first night in the tank.
The male freddy I found on Google images.
Funny enough, I had a similar conundrum id'ing the male loiselli when I first got him too. The general consensus from experts here at the time was what I've been calling the loiselli is a loiselli and what I've been calling the friedrichsthalii is a friedrichsthalii. So, that's what I've been calling them. Plus, I can say I've got four of the five parachromis, lol.

(soon to be 5 of 5)
For the record, I got both of them at another Asian fish store (different from the asian fish store I got the jag) at seperate times months apart and both were sold as "gold jaguars". My female loiselli has mated multiple times with both of these males if that means anything. No fry have resulted as the female has eaten the eggs each time before they hatch.
Long story short, I usually trust the experts around here. Sometimes with variations in color and body shape from one population to another makes it hard to exactly ID a fish. A good example of this is the pics of the "new" Parachromis sp. La Ceiba from fishfarm and others. Are they a loiselli? Or a freddy? Or an entirely new species? It's hard to tell exactly and only extensive genetic testing can tell for sure.
At the end of the day, both of my males we're talking about are definately Parachromis and they are super cool. They both have great personalities for my community set up and I've gotten to see both in breeding behavior. I just wish I could see some parental behavior with fry.