Many states regulate ammo. All the relevant lic laws in Illinois apply to ammo as well. You can't cary concealed period (with certain exceptions ie law enforcement). In contrast, Indiana has a constitutional amendment that mandates the issuance of carry permits to most persons. Carry permits require concealed.

I need to lock up and carry my weapons in my trunk in Illinois, cross state line, and I can stick them in my pockets.

Here is a fun fact, if you have been convicted of a violation of a domestic violence act (such as domestic battery) even if it is a misdemeanor (or less), then Federal Law prohibits the possession or ownership (or use) of any firearm. This includes hunting, target shooting, and killing rabbits. This applies also to law enforcement, and other unsuspecting individuals, and if your conviction was decades before the federal law was passed, it still applies to you.