How could there be two different Talmuds (Babylonian and Jerusalem) if they are both stemming from a direct oral tradition from Sinai?
In your question
How could there be two different Talmuds (Babylonian and Jerusalem) if they are both stemming from a direct oral tradition from Sinai? you seem to assume that the 2 Talmuds create 2 distinct sets of conclusions.
Actually, I'm not sure what you're asking - it seems you are lacking some fundamental information about the topic at hand. Here's some of that information:
The 2 Talmuds are very similar in their conclusions, on most issues. When they differ, Poskim (codifiers) will usually take both opinions into account before making a decision.
The main glaring difference is the Jerusalem Talmud being terser and records less back & forth.
I would venture to say that there are more internal arguments in the Babylonian Talmud than there are arguments between the 2 Talmuds.
They both stem from discussions on the Mishna. The Mishna is based on a direct oral tradition from Sinai that unfortunately got corrupted during the destruction of the 2nd temple, resulting in multiple opinions on many topics, which are the topic of most discussions in both Talmuds.
This answer is based on having reviewed Tractate Chagiga 100 times in the Babylonian Talmud and 30 times in the Jerusalem Talmud.