According to Wikipedia:
The Stolen Valor Act of 2013 was signed by President Barack Obama on June 3, 2013. The Act makes it a federal crime to fraudulently claim to be a recipient of certain military decorations or medals in order to obtain money, property, or other tangible benefit.
and the 2005 act
broadening the law to cover false claims whereas previously an overt act had to be committed;
So it would seem that the 2013 act punished a set of overt acts in addition to a claim whereas the 2005 act made the claim itself illegal. The courts ruled that a claim alone was speech. The courts did not rule on overt acts. Note that some overt acts would have been illegal prior to either law being passed. It's unclear what this would have changed in the test cases.
Note: this is based on no personal knowledge of either law. This is just what I'm reading. Perhaps someone else can offer a more thorough answer later.