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

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But how come the first one will not get an error since I am also assigning 0 to A initially. For the second case, I am just doing the same thing, but moving the resetting part to another sequential clock process.

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They are not the same, because the assignment to A in the first always block is always overriden, so A can only be in_u or in_v

In the second one, A is always assigned to 0, but it is also always assigned to in_u or in_v. In this case, if the selected signal is 1, then the 1 drives against 0 to give X