I found this . Might give a little help. It is German though. https://www.scribd.com/document/114121953/Vorsilben-II I could never come up with an explanation on my own :/ It says er- is indicating you achieve something through an action (with verbs), or a change in status like in erkälten, you change from healthy to one with a cold Be- is in general indicating some general adjustment, and the word with be- is changed in to a transitiv verb. ( A transitive Verb can use an accusative object.) Seriously I do not think that is a sufficient explanation. Imo it seems to be easier to learn them in context.. I guess I tried

Hi, each prefix has an initial root meaning but it's more conceptual than strictly defined you may find explanations in some grammar book (*) some verbs have kept the original meaning, some have evolved like in any language to learn them, you have to read books, listen to TV, practice with people (*) here is a good starting point https://en.wiktionary.org/wiki/be-#German

There isn't a simple answer, but maybe this helps a little: https://de.wiktionary.org/wiki/er- https://de.wiktionary.org/wiki/be- (I'm sure, there is more to say about these two prefixes than this ...) greifen / ergreifen: The prefix er- may give a 'subtle difference' in meaning, e.g.: Ich greife nach dem Bleistift. Ich ergreife den Bleistift. but there also can be new meanings: ergreifen also can have the meaning 'to apprehend' (pochwycić) https://www.duden.de/rechtschreibung/greifen https://www.duden.de/rechtschreibung/ergreifen