Samuel I. answered 07/18/20
(B.M.) Theory and Composition and 8+ Years of teaching experience
My view of these differences is, though subjective, that each one of them have different functions to serve the piece and the musicological intent, beyond just being "more" or "less" of an effect than the other.
For example, ritardando is more common and often seen that rallentando. Since we also know that in some way or another ritardando has a weaker effect than rallentando, then we can interpret that ritardando has a more "casual" function, and therefore should be very well blended with the phrase structure, and aid to the normal tone in which the music "speaks." Rallentando, on the other hand, is highly intentional in its function; therefore, you are more likely to want to make that rallentando stick out more in the periodic structure. The more intentional or less casual an indication becomes, the more of a special, contrasted effect it becomes. And that is how we get to Allargando, which to me is very similar to rallentando, but includes a broader spectrum of intentional effects to include in each instance (such as in articulation, rhythmic modulation, etc.).
Interpreting a piece of music is neither just the composer or just the performer. It should be a conversation between both of them. On one side, the interpreter has to be humble enough to educate themselves as much as possible with the composer and the piece, since the amount of genius and invaluable musical content that one can discover can often be very rich, and only be achieved by getting into the composer's mind and intent, as much as possible. On the other side, this never-ending journey of the interpreter's education enables him/her to finally start making a case/cases on their own and bring new things to the table. Just like with any other science, the right sources from other people/scholars are the best and most necessary foundation to start bringing the most acceptable and innovative ideas.