For starters, the guy who compiled that page is a conservative, and he kitchen-sink categorizes everything even halfway-related as "Welfare" because that's what conservatives have always done: gloss over the details to produce big scary numbers they can "sound the alarm" about.
Now, let's break down those number, shall we?
Social Security and Medicare take up the lion's share, but the only people who consider those "public assistance" are conservative/libertarian zealots bent on destroying them. But they'll happily blur the lines between those and more direct assistance in order to produce big scary numbers and create the impression that there's an army of layabouts sponging off the rest of us (and those eeeevilllll sooooooocialist Democrats who let them).
Medicaid also has a lot of users who aren't generally considered "on welfare." I'm thinking of the use of Medicaid to pay for nursing home/hospice care.
Unemployment is a sliver. Housing and Families & Children assistance, the stereotypical "welfare", are a fraction of the "TTTTRRRillions" and would be even smaller if wages hadn't effectively been stagnant for several decades.
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