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Just a bit curious how dice rolls are viewed IG, regardless if they are attribute, skill or saves, both by players and DM's.

(1d20 + modifier) = total

For example:

Character 1 (18 + 1) = 19
Character 2 (4 + 18) = 22

I guess my personal answer would depend on the skill involved. IC, you would see the person performing the task (if using Spot, the hand over the brow; tumble, a light dancing of the feet; etc etc). If the PC made a particularily good roll, I would assume you could see (in some cases) how well they accomplished the task. Enough that you could comment on it ("hey, nice save" --if it was a tumble attempt to avoid tripping over your shoelaces, e.g.). Other skills you'd have to see a lot, to know the PC was proficient in them ("hey, xxxx, would you mind using those eagle eyes of yours and tell me what you see?"). But on a casual, one-time observation, such things would not likely be discernable. And you certainly wouldn't be able to make anything but a very a general IG assumption (wow, this PC is even better than I am at [insert skill here], etc) from a one-time observation.

EDIT: And in your provided example, I don't think any outside observer could tell the difference between an unskilled person doing a great check, and a skilled person doing a lousy check. Unless they knew that person rather well, and it was the sort of skill they could openly recognize.

From a DM perspective if its a roll i ask for, its not something that the other PCs will notice UNLESS an emote is made with it.

If its a roll that the player wanted to make, there is usually an emote involved too so the other players can see.

With regards to what you can make out ICly. If its a PHYSICAL check (reflex, tumble, search, pick locks, etc) then you can see roughly how good they are.
If its a PERSONAL or MENTAL check (will, spot, listen, etc) then the other PCs WILL NOT be able to tell how good they are UNLESS the PC doing the check tells what they see or feel.