Both assert and verify commands are responsible for checking whether the given condition is true or false. However, the main distinction between the two lies what each of them does after the condition checking is complete. If the condition comes out to be false in the case of a verify command, then the execution stops and no further tests will be executed. However, if the condition is true then the program control will continue executing the next test step.
Verify command, on the other hand, does not care about the result of the condition checking. Whether it is true or false, the program execution continues and all the test steps will be completed.