Bill "Evolves" Between Congressional Vote and President's Signature

What happens when the Bill a legislature votes for is different than the Bill the Head of State signs?

A fascinating story is playing out down south: the U.S. Congress voted for a highway funding bill, which the President later signed into law.  But someone altered an "earmark" provision after Congress voted, so the bill the President signed was slightly different than the bill Congress voted on.   Specifically, a $10 million earmark was changed to redirect funds to upgrading an apparently useless stretch of road.  It turns out the locals don't even want the road built.

The Senate is seeking a federal inquiry  and Congress may seek a criminal probe.  Hopefully the constitutional aspect gets some consideration before (righteous) outrage drowns out the interesting constitutional aspect.  Is this rogue Bill a law?  Is what the President signed legally different than what the Congress approved?  What would the result be here in Canada, if a section of a regulation, for instance, was altered after a Parliamentary vote? 

One thing is certain: our friends down south will spend far more than $10 million getting to the bottom of this.

Enjoy your week,

Chris Graham