There are some semantic issues, e.g., the distinction between "mandatory" and "discretionary" expenditures, but the data is pretty easy to explore.

Essentially you are "both right". > 50% of total spending is Social Security, Medicare and Medicaid. Whether that is "social services" is another semantic question.

And > 50% of the discretionary budget is defense.

But have a look for yourself: e.g., https://en.wikipedia.org/wiki/United_States_federal_budget