Power
A security guard will have some limited authority over the people patronizing whatever location they're responsible for. A good command speaking voice is useful for this purpose.
"Freeze!"
"Don't touch that!"
"Step away from the painting!"
"Take one more step toward the vault and I will turn this Barry Manilow album on full blast!"
In the event of a security issue, it's likely the senior guard will have on-scene command until official authorities arrive, with the understanding that, as your company is being paid for its services, the individuals paying for said services do not expect to be victimized by them.
Plainly put, if you're guarding a department store and someone tries to shoplift, during the ruckus that follows, it would probably be a bad idea to accidentally tase the store manager as he's trying to help. At least, if you want to come back to work the next day, it's a bad idea.
But other than the above scenarios, and excluding any supervisory responsibilities within the company, a guard's power pretty much ends when their shift does.