あとで・てから: the difference
あとでN4
Meaning
After, Later
Past papers
Tested 2 times in past papers
Example
仕事の後で、飲み会に行きます。
I'll go to the drinking party after work.
てからN5
Meaning
Once...is done, Once...happens, After doing
Past papers
Tested 5 times in past papers
Example
日本語の勉強をしてから、日本に行きます。
Once I study Japanese, I will go to Japan.
How to tell them apart
「～たあとで」 only gives the order; there can be a gap between the two things. 「～てから」 is tighter and can also mean 'ever since': 「日本に来てから、ずっと一人暮らしだ」.
Even for the future, the first verb stays in the 「た」-form: 「明日、映画を見たあとで食事しよう」, not 「×見るあとで」.
「～まえに」 is the opposite and takes the dictionary form.