Hard money may or may not be institutionalized. Hard money vs private money is really more of a professional vs amateur thing.
Hard money lenders are pro's. We do it for a living. Most use institutional funds for their loans. Some of us also help place money for private people.
Private lenders are typically people who lend money, but it's not a full time gig for them. They are also not as educated. Most don't truly understand the legalities of things and many new lenders don't know how to secure their funds properly.
Both can be good sources of capital. It just depends on what you need and whether or not you know enough to take care of your private lender properly. If you use Hard Money, the broker/lender will take care of everything. If you are borrowing private money, it becomes your responsibility to make sure that you hook them up with a good attorney who can draft their paperwork properly. NEVER DO THEIR PAPERWORK FOR THEM. if you do the paperwork for them, you can get into a lot of trouble for practicing law without a license. You could get away with it for a while, but if a deal ever goes sideways and they hire an attorney to help fix the problem, it won't go well for you.
I have quite a few borrowers who have found private money, but they referred them to me for help. If you don't have an attorney who understands lending, it is a lot safer for you to send them to someone who can help them properly. In my area, there are few attorneys who really understand what we're doing and how to protect their clients properly.
Good luck!