Silly me, I thought you were asking why someone would have both, when you were asking what's the difference between the two programs.
Medicare is based on payroll taxes and is largely for retirement, although disabled people can receive it too, if they either worked enough before they became disabled, or if they became disabled before they turned 25 and had an eligible parent who is dead (then they get the dead parent's medicare). Medicare does not make any cash payments to the recipients, only to health providers.
Medicaid is need-based and anyone with a low enough income can receive Medicaid, including illegals nowadays (although they used to be ineligible THANKS OBAMA). Medicaid does not make any cash payments to recipients, only to health providers.
Social Security is a payroll tax based pension plan. Anyone who works long enough and pays enough taxes is eligible to receive cash payments once they retire. Some disabled people are eligible, and children who have a parent die before they're 18 can receive the dead parent's benefits. Social Security payments are based on what was paid into the program in the past and are generally small, less than $1500 dollars a month.
General assistance is traditional welfare. It makes cash payments to recipients based on low income. Usually able-bodied men are not qualified for General Assistance. General Assistance is now only available for a limited period of time, in most jurisdictions, 5 years or less. Recipients who have collected General Assistance until they're close to timing out are routed into the Welfare to Work program, a jobs training program that will assist the recipient in finding work and even provide job placement services for them. This is how people at the Goodwill get jobs as cashiers. Basically only single mothers with multiple children qualify for General Assistance.
EBT is a food assistance program based on low income. Recipients are given benefit money on a special debit card and the money can only be spent on cold food items. Fast food places like McDonalds or KFC cannot accept EBT money. General Assistance money can also be distributed to the same card if the recipient is eligible. Far more people are eligible for food assistance than general assistance so the majority of EBT cards are food cards.
HUD Section 8 is an income based housing program for low income families. Based on local fair housing prices, recipients are offered a grant that makes up the difference between what they can afford to pay and what housing really costs in their area. For instance, the if fair housing price for a 2 bedroom is $1200, HUD pays $900 and the recipient pays $300, so the landlord still gets $1200. There are a number of ways it can be spent. One way is the recipient can rent an apartment in a low-income housing development (project). Nowadays a lot of developers are forced to provide low-income units in order to get the permits to build large condo developments, so a condo complex will have 80 full-price units and a block of 20 low-price HUD units in order to meet the county's demands. Or, the recipient can find an available housing unit anywhere in a city in which the landlord will accept HUD. HUD pays the money directly to the landlord. There are certain requirements of HUD recipients in order to keep qualifying, one of which is they must keep the place clean and habitable, they aren't allowed to let others move into the unit, and if they get arrested for drugs they lose their HUD. A lot of landlords don't take HUD because of the red tape involved and the general flaunting of the rules.
If you have any more questions about gibs I will try to answer them in this thread.