That I'm having to work part-time while building my own business only means that I'm not a self-sufficient entrepreneur yet.
In my case I am living of the money from a previous exit.
Similarly, I love money very much, but I'm not obsessed with it. I'm more into making things. So I guess designer, if anything?
When our current business started growing rapidly/accidentally, we sold our previous business simply because we didn't have time to do both. We sold it for enough to pay off our SBA loan and take home a little extra money.
Otherwise, you might end up burning a bunch of years of your life coasting by and then realize "why haven't I made any really cool stuff yet?!?"
As for hackers, I have a very inclusive definition: someone who likes to tinker with code or other technical stuff without the need to get some gainful result from it. People who code at work and then clock out and turn off completely, for example, do not fit the definition.
If you have some other people working for your web development business and you can go to the Bahamas for 3 months without your business going down the toilet, then you're an entrepreneur.
But I think most people on HN will think of an entrepreneur as someone who builds a product that has its own value, and you can sell the product to multiple people to earn money. Or generate repeated advertising revenue.
So I think entrepreneurship is creating something (a product or a service) that leverages your time so that you don't have to work some part of an hour for every dollar you earn.