What's the difference between Public Housing and Section 8?

I’m looking to move into an apartment and I also have a tremendous amount of debt to pay off with a $3.30/hr pay decrease. I’ll only be making roughly $17,000/year. I’ve thought about looking into applying for housing assistance until my situation is more stabalized. I’m having trouble clarifying some of the information I have found online. I live alone, according to charts I’ve found, I am able to qualify for both. Have also seen credit and rental history is taken into account as well. Can anyone provide advice as far as what may or may not be the best option between Public Housing and Section 8?