What's the difference between these two pieces of simple code?

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Okay, so that simply means:

1) Assignment in different 'always' blocks --> they are evaluated in parallel, resulting in multiple driver error

2) Assignment in the same 'always' block --> they are evaluated in sequential, where it will reset initially before going into a MUX

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You need to understand the underlying hardware.

1) It generates 2 bits of logic that have both outputs wired together. Each always block creates some logic.

2) Yes - but there is no reset occuring, because the assignment to 0 is overriden and thus ignored.