Use the word formally when you want to describe actions that are carried out with formality or official procedure. This can refer to being dressed in formal wear for a special occasion, like a ball or gala, or official actions taken by organizations or institutions, such as formally adopting a policy.

The word formerly is used to talk about a previous condition or state of affairs, often pointing to a contrast with the present. It can refer to a person's previous job or title, or the past use or name of something.

In summary, formally and formerly are adverbs that serve distinct purposes. Formally is employed when referring to actions carried out with official protocol or etiquette, emphasizing the method and manner of an action. Formerly, on the other hand, is used to indicate a past state or position, linking to a time before the present. Recognizing the context in which each word should be utilized is key to their correct application.