Sight-singing is looking at written music and producing the pitches / rhythms / lyrics / etc. that were written.
I’m terrible at rhythm / lyrics and don’t even think about being expressive or having a nice tone. I think this is because I started sight-singing on the car ride home from piano lessons: when I got assigned new music, I was usually so curious to know what I’d gotten that I couldn’t wait to get home to hear it. Instead, I just hummed it out to the best of my ability.
I didn’t sing words or syllables (everything was just a hum), and usually if I could recognize the melody, the rhythm would come (as well as implied harmonies; I guess I never got anything with really surprising harmonies).
I’ve looked at Modus Novus a little bit, for atonal things. I like singing perfect fourths a bunch of times until you reach the note a half step above the one you started on (so you can check yourself).