Yeah, living in a parliamentary democracy means I have to make an effort to wrap my head around how the US "democratic" institution works. The internal structure of the Democratic Party has more in common with our democratic structure than the structure of their "competing" parties. As a result there is more room for difference within the Democratic Party than within a political party in our system, but the political difference between parties in our system is greater than those within the democratic party.
Whilst it economically is to the right, many of its social policies it endorses are leftist.
My analysis has long been that there is no political will to implement leftist economical policies in the US, i.e. those that really matter in the grand scheme of things, even though there exists a semi-conscious wish for them within the populace. Please do not misunderstand, increasing equity between people of different backgrounds is important, but important single issues such as gay marriage are insufficient if they do not come along with, or better yet, as a product of equity of material conditions. It was all the same with the feminist movement where social advancements were conceded in lieu of increasing their economical statuses, with the division in measurable quantities, such as income or capital ownership still going strong (note I do not advocate changing the ruling elite from one subset of people to another subset of different characteristics, but instead saying that capital ownership should be transferred from the subset to the whole).
Strengthening the political power of the marginalized by increasing the material conditions of their strata is the best way to make social progress, which the ruling elite of the US is painfully aware and which is why they sometimes are willing to skip the first step and reach the inevitable second immediately. The discrepancy between the people's wants and needs for leftist policies, again conscious or not, and the actual politics of the US, is deeply connected to the Democratic Party's willingness to concede these social changes without losing the backing of the capital interests that fund them.