The dual-taxation fix is the part most workers actually use, and it runs on a certificate of coverage. When an employer sends an employee to work temporarily in the other country, the agreement typically keeps the worker under the home country's Social Security system for a set period, often up to five years, under a "detached worker" rule, so neither the worker nor the employer pays into the host country's system for that assignment. To prove the exemption to the host country's authorities, the worker obtains a certificate of coverage from the country whose system continues to apply. For people who are not on temporary assignment, the general rule assigns coverage to the country where the work is physically performed. Either way, the outcome is that the same earnings are taxed for Social Security by one country, not two.
The credit-combining fix helps people whose careers were split. United States retirement benefits generally require 40 credits, about 10 years of covered work. Someone who worked six years in the United States and the rest of a career abroad would fall short of 40 and, without an agreement, get nothing from Social Security despite having paid in. A totalization agreement lets the Social Security Administration count the foreign credits toward US eligibility, provided the worker has at least six US credits of their own, so the person can qualify. The foreign country does the mirror image for its own benefit.
A totalized benefit is prorated, not doubled. Combining credits establishes eligibility; it does not inflate the benefit. When the United States pays a benefit that only exists because foreign credits were counted, it pays a "totalization benefit" computed on the US credits alone, prorated to reflect the share of the worker's career that was covered by US Social Security. So a worker with just enough combined credits to qualify receives a partial US benefit based on their limited US work, and separately may receive a partial benefit from the other country based on the work done there. The two systems each pay for their own portion; neither pays for the other's.
It is not a tax treaty and does not touch income tax. A totalization agreement addresses only Social Security taxes and benefits. Income taxation of cross-border earnings, withholding on investment income, and the residency questions that go with them are handled by a separate income tax treaty, if one exists. A country can have a tax treaty with the United States, a totalization agreement, both, or neither, and the two are administered by different agencies.