https://en.bitcoin.it/wiki/Difficulty
There is a linear relationship between the hash rate and the difficulty (there is further discussion at that link).
It's in your last sentence that you go wrong. There's a relationship between the number of expected hashes per new block and the difficulty. That tells you something about the hash rate, but not the rate itself. Actually, it tells you something about the number of unique hashes being tried per new block (in expectation). And for some applications, that may, in fact, be what you care about.
Specifically, the appearance of new blocks is, if you like, a random variable with an exponential distribution. You can, in principle, estimate the rate parameter for this distribution using the difficulty and the timestamps in the Bitcoin log, but it's not straightforward. The last time I got into it, I was halfway through building a Bayesian estimator for the rate parameter using the log before I had to give up and move on to real work. I'll do it soon.
In what applications would the likely immediate hash rate be more useful than the historical average hash rate? I guess the obvious one is turning some bit of mining hardware on and off.