Sanders claims to be a Democratic Socialist. This is a variation on pure Socilism which postulates that both the economy and society should be run to meet public needs, not to make profits for a few, in order to achieve a more "just" society.
It doesn't necessarily call for public ownership of the means of production but it does believe in government regulation of private corporations.
I put "just" in quotes because that's usually the stumbling point. Who defines what is "just?" The simple answer is it's determined by who the people elect. I think it's safe to say that Republicans and Democrats in today's society disagree on what is "just."
I think most political scientists would consider the current US a "mixed economy." Primarilly Capitalist but with some Socialist like concepts such as significant government regulation, Social Security, Medicare, SNAP and Medicaid among others.
A major problem of course is that the US government has no significant source of income other than taxation since it doesn't own any means of production. That means the government doesn't actually pay for anything but acts as a middle man that makes Tom and Dick pay for Harry's benefits.
Needless to say that often doesn't please Tom and Dick.
Republicans tend to want to push things more toward Capitalism under the theory that will result in a stronger economy and benefit everyone. The Democrats believe that society needs a government safety net of some sort because regardless of how strong the economy is there will always be people on the outer edge of society that require government aid. Therefore they tend to try and push more toward more Socialist like programs.
For the past 80 years or so there has been a steady but ragged movement to the left and I don't think that going to change any time soon. Sanders is trying to jump to where we might be 50 or 60 years from now and I'm pretty sure that's not going to happen.