Does the word "legitimization" refer to the process of affirming an out of wedlock relationship?

It means to Make Something legal e.g a document etc

legitimisation is to make legally acceptable.. Depending on the country you live in an out of wed lock relationship may not be recognised in the country's law. This would mean that the partners in the relationship woyuld not be eligible for the same benefits as a married couple.In such a case, you might legitimise the relaionship by a civil marriage or a religious ceremony.

Legitimation is the act of providing legitimacy.

Legitimation refers to the process whereby an act, process, or ideology becomes legitimate by its attachment to norms and values within given society.

It is the process of making something acceptable and normative to a group or audience.