Both phrases/sentences express same meanings
1: Sending json data to postgres once received from API

2: Sending json data to postgres after receiving from API

3:Sending json data to postgres once it's received from API

Question

Both phrases/sentences express same meanings
1: Sending json data to postgres once received from API

2: Sending json data to postgres after receiving from API

3:Sending json data to postgres once it's received from API

Answer

Yes, they all have the same meaning.
The 2nd phrase (if part of a sentence and not just a summary phrase) would read better if you replaced 'after receiving' with 'after receiving it'.

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