Code Share Flight with different ticket prices
 

I am trying to book a flight from ewr to lax and see an American Airlines flight that is also labeled an Alaska Airlines flight. The tickets are cheaper if I book through Alaska Airlines. Why would this be and if I book through Alaska Airlines could I still get American Airlines points for the flights since they are operating the flights??

Each airline is free to set their own fares, and availability may differ (eg AA sell out of their cheapest fares before AS on this particular flight).

I booked a AI codeshare on TG that was in place the days AI didnt fly its own metal. The codeshare was about 140$, the TG coded was about 650$

Yes - But look carefully at the fare class. For example, if you fly a United Airlines flight number on Air Canada metal you may wind up in an Air Canada fare class that doesn't earn miles. I'm not sure if the same applies here.

The main issue with code-shares is if something 'goes wrong' i.e. there's a cancellation or your need to change your flight. On more than one occasion I've found myself ping-ponging between the two carriers, with each one saying it's the other carrier's problem.

Code shares have been around for decades, but it seems the airlines are still trying to 'work out the bugs.'

You can still get AA miles, but only according to Alaska's rules, i.e. because Alaska allows you to accumulate AA miles on their flights. There are certain times where that don't necessarily apply (for instance, you probably couldn't accumulate AA miles on an Alaska-coded flight operated by Northwest) but you should be OK here.