Both are federal Direct Loans, but the government pays the interest on subsidized loans while you're in school at least half-time and during deferment. Unsubsidized loans accrue interest from the day they're disbursed — interest that can capitalize if unpaid.
Direct Subsidized and Unsubsidized Loans are both federal student loans issued by the U.S. Department of Education with the same fixed interest rates (set annually by Congress), the same repayment plan menu, and the same path to forgiveness programs. The single most important difference is who pays the interest that accrues while you're in school: for subsidized loans, the federal government does; for unsubsidized loans, you do — or it adds to your balance. Full details at studentaid.gov on loan types.
Direct Subsidized Loans are available only to undergraduate students who demonstrate financial need, as determined by the FAFSA. While you're enrolled at least half-time, during the 6-month grace period after leaving school, and during authorized deferment periods, the Department of Education pays the interest that accrues. You graduate (or leave school) owing what was disbursed — not more — assuming you don't capitalize. Subsidized loans come with annual and aggregate borrowing limits.
Direct Unsubsidized Loans are available to undergraduate, graduate, and professional students regardless of financial need — no need-based eligibility requirement. Interest starts accruing on disbursement day. While you're in school you're not required to pay it, but unpaid interest can capitalize (be added to your principal) when you enter repayment, creating a larger balance than what was originally disbursed. Paying interest during school — even in small amounts — reduces capitalization. Graduate students typically borrow exclusively through Unsubsidized and PLUS loans, since Subsidized Loans are not available for graduate study.
If you borrow unsubsidized loans and make no interest payments during a multi-year degree, the accrued interest can capitalize at repayment — meaning you start repayment owing more than you borrowed and pay interest on that interest. Paying even small amounts toward unsubsidized interest while in school can prevent hundreds or thousands of dollars in capitalized interest. The studentaid.gov loan simulator can show projections for your loan amount and rate.