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After 1.e4 e5 what are the ideas behind 2.Nc3 versus 2.Bc4?

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1. e4 e5 2. Nc3 (2. Bc4)
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The Bishop's opening:

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1. e4 e5 2. Bc4

https://en.wikibooks.org/wiki/Chess_Opening_Theory/1._e4/1...e5/2._Bc4
In low elo online chess 2.Bc4 often indicates that white wants to play for scholar's mate (3.Qh5) and will set a series of traps that lead to a win or a material advantage. It is considered dubious and black has good chances of equalizing or gaining a winning advantage.
Scholar's mate is not the only option, and there are legitimate lines to be explored from this position.

The Vienna Game:

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1. e4 e5 2. Nc3  

https://en.wikibooks.org/wiki/Chess_Opening_Theory/1._e4/1...e5/2._Nc3
This has various lines to explore. I don't play this opening so I cannot explain any ideas to you. A popular variation is the Vienna Gambit, which is known to provide winning chances for both sides, depending on the elo of the players.

It is to be noted that both moves can transpose into the same position

[FEN ""]  
1. e4 e5 2. Nc3  (2. Bc4 Nf6 3. Nc3) Nf6 3. Bc4

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