Alright, but only because I'm avoiding doing actual work...
The F22 engine (Pratt & Whitney F119) produces 156kn of force. Badass. The Lunar Ascent Module Engine (we'll call it LAME from now on) produces... 16kn of force. Wamp wamp wamp. As you put it, the idea that they're remotely the same is laughable; LAME is about 10% as cool as the F119. So what gives?
Because the moon has no drag (atmosphere) and the gravity is 16% of Earth, you don't need a big huge rocket; you just need an efficient one that you can sustain. The gravitational force is only (1.6m/s^2 * 4000kg) 6.4kn, or 40% of LAME. LAME is only about 1/3 the size of the descent engine! Why? It only has to carry about 1/3 of the weight back. The F119 fires for many hours; LAME only fires for minutes.
Since you like pictures, here's one of the wimpy bastard compared to the descent and maneuvering engines:
http://history.nasa.gov/SP-350/i4-9.jpg
Again, I have no idea if Apollo 11 landed on the moon or not. I don't really care; it wouldn't be the first time the government lied to us, so it isn't an important proof-of-concept. Regardless, the idea that the landing is somehow scientifically impossible is just not correct.