Respectfully is used to demonstrate consideration and honor towards someone or to express a formal gesture of politeness. It is often employed in formal correspondence and settings where deference is warranted. For instance, ending a formal letter with 'Respectfully yours' indicates politeness and a respectful tone.

Respectively is used to specify the individual relationship between multiple sets of items. It should be used when there are at least two sets of items being discussed, and there is a need to make it clear which items from the first set correspond to which items in the second set. For example, use respectively when stating that Alice and Bob won first and second place, respectively, to indicate the order of the winners.

In summary, respectfully and respectively serve distinct purposes in language. Respectfully is employed to demonstrate reverence and courtesy, especially in formal communications. It adds a tone of esteem to an action or statement. Contrastingly, respectively is used to relate parallel lists or sequences, ensuring readers understand the order in which corresponding items are referenced. Mastery of these terms allows for precise and respectful communication. Remembering the 'full of respect' meaning for respectfully and the sorting function of respectively can help avoid confusion between the two.