How Does Alternation Differ From Boolean Or?

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I am trying to write a Regular Expression to read real literals based on this graph: Regex Graph
I found that this solution works:

([0-9]+(\.[0-9]+)?[Ee][\+\-]?[0-9]+)|([0-9]+\.[0-9]+)

Notice the two parts separated via alternation:

([0-9]+(\.[0-9]+)?[Ee][\+\-]?[0-9]+) 
([0-9]+\.[0-9]+)

When I tried to switch the order of which one is on which side of the alternation symbol, it stops working

([0-9]+\.[0-9]+)|([0-9]+(\.[0-9]+)?[Ee][\+\-]?[0-9]+)

These parts are exactly the same as above, but now it's suddenly not working. Am I misunderstanding how the | (alternation) symbol works? Is it not the same as || (or) for boolean expressions?

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