Ordinal logistic regression vs. multiple regression with ordinal outcome?

I have a basic question about Ordinal Logistic Regression (OLR),
which is logistic regression with an ordered-category outcome
variable.

Please excuse any incorrect statements below--it is my very
ignorance about logistic regression that prompts the question.
I believe there's a simple answer, and perhaps someone can
supply a concise one. (Also, I hesitate to mention this, but
experience suggests I should: no rambling, speculative replies,
please!)

It seems to me OLR assumes something like one of the following:

1. The odds of going from one outcome level to the next higher
one are constant (or proportional?) for each pair of
adjacent outcome levels.

Or possibly:

2. The odds of going to outcome level j from *any* lower
outcome level is constant for all levels j (cumulative
logit?)

Whichever the case (but it appears more applicable in case 1),
how different is that from assuming that the outcome variable
levels are evenly spaced in the first place--i.e., an interval
level of measurement. But in that case, why not just use
ordinary multiple regression?

Thanks in advance.
--
John Uebersax, PhD

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