January 17th, 2016, 11:22 PM
Join Date: Dec 2008
Location: In the Heart of Dixie, Alabama!
US M-1 bayonet for the M-1 Garand, so yes it is correct. The looseness you mentioned is normal. These were made to be fairly loose as a tight fit will adversely effect the bullet's trajectory.
Yours looks to be an Utica Cutlery due to the U C stamp above the flaming bomb (WW II Ordanence Department acceptance stamp). It appears to be in decent but we'll used condition. Replacement grip panels are available through many sources, with a little work and a good Parkerizing you'll have a nice addition to your rifle.