Ritardando and rallentando both mean gradually getting slower and according to my AB guide to music theory book they are both supposed to imply a gradual slowing down. And allargando means broadening, implying getting a little slower and probably also a little louder.
Without a doubt execution sometimes changes in some cases, since words can change meaning over time. For example, ritenuto originally meant an abrupt change, although now it carries the same meaning as rallentando or ritardando.
However, to my knowledge and access to information, I could not find any reliable citation anywhere that states that rallentando and ritardando may be interpreted differently. However, there is this blog where some worthwhile digging around has been done and the researcher indicates that there may be a subtle difference between the two words, as they are two different words of the Italian language. From an Italian-English dictionary the author found:
Ritardare: “be late, wait, retard, lag, stay, lose, delay, set back, defer, put off.”
Rallentare: “slow down, reduce speed, slacken, slow, die down, decelerate, check, put back.”
This implies that ritardando seems to be a deliberate slowing or being late, while rallentando seems to be more of a letting go or dying away.(although it becomes similar to smorzando and raising the same question all over again).
Therefore, I come to the conclusion that composers may have used all three words differently but what the differences were, especially between rallentando and ritardando (discounting allargando as my book has given distinct directions on that), might be too subjective and individual specific to define properly and therefore, if one must be pedantic, it is best to leave it to experts who have studied the composer to give the final opinion. The blog gives an idea on this. So yes, it should vary slightly not just from era to era but also from composer to composer.