Hardee's was a separate company that was bought by CKE in the late 90s. The midwest and west franchises in Carl's Jr regions were sold to Burger King by CKE (not perfect, see the map below), which kept the Hardee's name in the east. CKE is the company that owns Carl's Jr. CKE irregularly upgraded the Hardee's menus to be similar to Carl's Jr in some respects. Apparently to this day they're a bit of a bastard child of the merger with their menus varying wildly by location and local ownership.
CKE changed their logo and most of their menu, but the menu/food is not actually the same as a Carl's Jr. Hardee's is basically their cheap eastern US variant that more accurately reflects the (lack of) taste of the people in the east and south.
Map of Carl's Jr (yellow) and Hardee's (red) regions