To me Saimin is a little more saltier and broth more clearer. Ramen a slightly darker broth. Never heard of ramen until I met my wife of japanese decent in california.
I remember 25 cent for a large bowl of saimin. A nickel more you get won ton min.
Saimin is a local invention using chinese noodles in japanese broth. It usually has fishcake, char siu, egg, and green onion as garnish.
Ramen is a Japanese noodle dish. Miso broth, or Shoyu/Salt broth are the two basic variations and there are a range of common garnishes.
check out this thread from a couple of years ago http://chowhound.chow.com/topics/618136