At some modest risk of over-simplification I'd suggest that the political right thinks of the Declaration of Independence's "All men are created equal" phrase as meaning equality of opportunity, while to the political left it means equality of outcome or condition.
This explains why the recent "spread-the-wealth" comment during the mercifully-just-finished political campaign drew both the negative response of the right and the fervent support of the left, because it addressed the re-distributionist goal of equal financial outcomes and rejected the concept of individual opportunity to compete, succeed or fail to greater or lesser degrees, and thereby create unequal financial outcomes.
It also explains such phenomena as the recent public-schooling interest in something called Outcome-Based Education, which seeks to have all students demonstrate, via preferred portfolio or less-preferred testing, the same outcome-level of content mastery, as opposed to traditional education which seeks primarily to equalize inputs even though differently skilled or motivated students will individually do better or worse with the same level of, for example, per-pupil funding. You can read a more detailed explanation of outcome-based versus traditional in Wikipedia.
As history in Vermont actually played out, the temporary infatuation of edu-crats with OBE, primarily in the '80s, was swept aside in the '90s by a left-dominated Vermont State Legislature in favor of a less Leftist and more traditional equality-of-input (funding) goal, which was made more attractive to them by packaging it in a state property tax which, for the first time in history , would reverse the budget-first-rate-setting-second principle to one in which assessment and rate (and therefore total tax) are arrived at by government independently of any voter-approved spending plan, thereby encouraging spending to rise as long as rapidly increasing property values triggered constant upward re-appraisals and collections, and only pennies in occasional legislative-ordered rate reductions.
OBE hasn't permanently gone away; in various states and cities, edu-crats are now arguing that in the pursuit of equal outcomes some school districts need more money-per-pupil than others, so that their lower-achieving students can supposedly be made "equal" to their higher-achieving non-peers in adjacent districts. For now, however, the Left in Vermont is more enthusiastic about equality of dollar input (raised via a policy of tax-the-rich-towns-to-subsidize-the-poorer-ones) than the equality of educational outcome.