Both SS and SSI benefits have the same requirements for disability–the inability to work at a suitable job for a continuous period of twelve (12) months or more. SS benefits (also called Title II) are based on the amount of SS taxes you have paid in the system for the ten (10) year period before you became disabled. SS benefits are generally higher than SSI benefits. Dependents of SS recipients may also be entitled to benefits. You should report any dependants to SSA even if they do not live with you.
SSI benefits (also called Title XVI) are based on a financial need. You may be eligible for SSI benefits even if you have never worked or paid SS taxes in your life. Generally SSA will sort out whether you are entitled to SS or SSI when you apply. In some cases, you may be eligible to receive both SS and SSI benefits.