Um . . . I'm glad to help when I can, but believe me, there are _others_ on this forum who just flat out know more or *different* stuff than I do.
I'll try with this one, though I compose rhythm patterns a little differently than most people.
Your questions:
"Maybe I'm applying it wrong."
Maybe, but we have no way of knowing without sitting there with you. Remember, too, that there are 3 different kinds of quantize. Read about the types in the manual and make sure you're using the most appropriate one for your problem. [I've never used Groove Quantize even once; I have no clue about that.

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"What would be the optimum type and settings to correct slight errors?"
Without knowing what kind of rhythm track you're working on, I would guess Grid Quantize.
If you use Grid Quantize, the two most important settings are (1) Resolution and (2) Strength. Read about those in the manual.
(1) Your "slight discrepancies" may be missing the Resolution. The smaller note (e.g., an eighth note is smaller than a quarter) may not "jerk" the discrepant note far enough to where you want it; it may only "jerk" it to the next eighth note position in the measure, and that may not be far enough for you. Your Resolution is too small. Try the next resolution up, in this case a quarter note. Or just the next resolution up from where you were.
(2) The Strength may also not be set high enough. Setting it to %50 will only "jerk" your discrepant note half the distance to whatever Resolution you set. 100% will put it right on the next closest (forward) note position of that resolution, e.g., right smack dab on the next eighth note position.
If you're unsure you're hearing any change, tweak those two values. If you're still unsure, do a quantize edit, then look at the note(s) in microscope mode: Are they were they were before? Did they move forward? By how much? Are they right on the next note position set by your resolution (e.g., right on the next eighth-note position?)
Remember also that you can preview the result while quantizing. See the manual.
If they haven't moved, you need a resolution up higher than the note value you chose, or a strength higher (or closer to 100%).
Also, make sure you are Setting your Note Range to include the notes you want, or rather: to include *only* the notes you want. If you don't include them in the Note Range, they won't be quantized. If you include *every* note in your pattern, every note will get quantized. Be careful.
After fooling with Grid Quantize a while, esp. at 100% strength, you'll get to know the clocks/ticks at which certain note positions occur, e.g., eighth notes quantize at 100% to ticks 24, 48, 72, and 96, etc.
You can then easily check how far your discrepant notes have moved.
Good luck. It's still a bit difficult to know at a (cyber) distance just what you are doing.