Generally speaking, no, a person cannot receive both Social Security Retirement payments and Social Security Disability payments. The reason for this, in theory, is that an individual is either not working because he is disabled or he is not working because he is retired (not both). In fact, if you receive Social Security disability, you will automatically be switched to retirement when you reach your personal retirement age. Retirement age is determined by when you were born.
There is one exception to the general rule that you cannot receive both retirement and Disability at the same time. If you are receiving partial retirement, which can begin at age 62, then it is possible to receive some retirement and some disability payments. However, the payments you receive for each are likely to be reduced to compensate for the fact that you are receiving both. This situation can get very complicated and can vary person to person. It is a good idea to talk to someone experienced in the process.