Brad,
Frederick W. Hamberg joined Co K 10th IL Infantry at Edwardsville, IL Oct. 1, 1861 for three years as private. Joined by Cpt Lusk. Mustered in at Bridgeport, AL. Transferred to the 60th IL Inf March 1864. (info from the 10th IL Inf). He was b. in St. Louis, MO, age 21, 5'5 5/8", brown hair, blue eyes, fair complexion, single, farmer. Gave residence as Edwardsville, Madison Co., IL.

60th IL Inf.--(instead of being transferred, he re-enlisted as a Veteran Volunteer) Joined as private Company G, 60th IL Inf. Feb 18th 1864 at Rossville, GA by Lt. Campbell for 3 years. Mustered in Feb. 22nd. Mustered out July 31, 1865 at Louisville, KY by Capt Papst. He listed age as 23, 5'6" tall, dark hair, gray eyes, fair complexion, farmer, b. St. Louis County, MO. Gave residence as Nashville, Washington Co., IL.

So the tag would mean he served in both---Co K of the 10th IL Infantry; and 60th Illinois Veteran Volunteer Infantry.

It was quite common for men to serve in Illinois in more than one regiment. Also, the place of residence often depended on not where the person actually lived, but where they were being recruited/enlisted from.
Hope this helps!!
Ann