Terrorism is about a political goal. I think I prefer my second definition a bit more. Thugs are thugs because they can get away with it.
I offer an alternative definition:
A "thug" is someone who believes in the morality of "might makes right" and seeks to impose his own will, whatever that happens to be, on other people in his life through force, threats, intimidation or violence.
Consider the following:
Put another way: a "thug" is someone who achieves his ends by bullying others into cooperating with him or physically dominating them if they refuse. It's the dimension of violence -- implicit or in action -- that defines the term. That's why the Gestapo and the Klan are often branded as "thugs" and even "terrorists" while police officers, who NORMALLY try to use words to resolve conflicts, rarely do.