I don't see the difference?

The difference is whether the violence is conducted within the established framework of international law.

America (or any country) is a legitimately recognized and lawful States holding sovereignty. When such states "go into other countries and kill people" it is called war; and is subject to international laws.

When individuals or private organizations "go into other countries and kill people" is called terrorism or murder (dependent upon methods/aims/etc.). That is a domestic crime and subject to the laws of the State in which the crime is committed.

That's why they are classified differently.

Perhaps you don't agree with this distinction. In which case, you should begin petitioning the UN immediately.

Terrorism is the systematic use of terror, especially as a means of coercion. Common definitions of terrorism refer only to those violent acts which are intended to create fear (terror), are perpetrated for a religious, political or, ideological goal; and deliberately target or disregard the safety of non-combatants (civilians).

American soldiers fight these people for your goddamn freedom. They fight so that you can be safe in your home, sit at your computer, and wonder why they are not "heroes". They are heroes. American soldiers are not ordered to purposely kill non-combatants in order to create fear in a country because we believe they are doing wrong. If a terrorist ever raids your home or your country you'll be screaming and crying as to why the army isn't there killing them. Be glad you don't know what it's like to live in a war-torn country.

Have some respect for the people who protect you.

What side are you on? Pick one.

Only people that have never had to lift a finger in their own defense (especially people like you that live in a country where others do it for you) have the luxury of asking such questions.

And come back again and ask this when good ol ' Mullah Akbar finally has one of his men get through thr border and suicide bomb your kid sister's elementary school

What would your thoughts be then?

The intention.

please read Geneva Conventions on Lawful Combat.