but I don't exactly see it that way because each mining node is competing against all the others.
There is no competition. Every hash found has an equal chance of matching or exceeding current difficulty, which is around 39.5 Billion.
If there's no competition, then why am I not solving ALL of the blocks?
Besides this, more importantly, each hash (ie difficulty of 1) has the same probability of solving the block as 1/1024 of a miner hashing at difficulty of 1024 (accepted share with difficulty 1024)?
And when my miner has difficulty set, there are no accepted shares below that difficulty. So I'm assuming that 934/1024 doesn't show up, because it's not accepted. My understanding is that 1024 is a larger fraction of 39.5B to be solved.