I am assuming you are asking strictly about startups and not other established non-profit companies or organizations.
Rob makes a very good point in that there social-mission startups that also have a profit motive.
So, for now, let's agree to simply call these two types you are trying to distinguish social versus economic startups. The social-mission startup is not typical of most startups and only now becoming more prevalent. The economic-mission startup is the one we still consider the more typical and its mission, instead of being social, usually is centered on pure free cash flow and growth, economic success, along with other aspects concerning stakeholders and community.
In both types of startups, there are many types of founders but let's break the founders into two broad types:
1. The mom-and-pop company type founder who is aiming to keep him/herself and perhaps a small group occupied and earning enough for a nice life. Sometimes these are the more locally focused companies, but not always.
2. The founder who is more typically thought of as the entrepreneur, who has some greater and glorious view of growing something of outstanding significance, something that will be disruptive in accomplishing its mission, in the extreme, establishing a new order.
So, again, both of these broad stereotypes exist in both social-mission and economic mission startups. No matter which stereotype they exist within, they are the same.
The only difference between the two is their mission - that's it.