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The And operator will check all conditions in the statement before continuing, whereas the Andalso operator will stop if it knows the condition is false. For example:
if x = 5 And y = 7
Checks if x is equal to 5, and if y is equal to 7, then continues if both are true.
if x = 5 AndAlso y = 7
Checks if x is equal to 5. If it's not, it doesn't check if y is 7, because it knows that the condition is false already. (This is called short-circuiting.)
Generally people use the short-circuiting method if there's a reason to explicitly not check the second part if the first part is not true, such as if it would throw an exception if checked. For example:
If Not Object Is Nothing AndAlso Object.Load()
If that used And instead of AndAlso, it would still try to Object.Load() even if it were nothing, which would throw an exception.