Sir, that's an M1 bayonet and cut-down M3 scabbard. The M1 bayonet was adapted from the 16-inch M1905 bayonet designed for the '03 Springfield. It fits both fits the M1 Garand and '03. The chief differences between the M1 and M1905 are blade length, scale (handle) material, finish, and markings. M1905s were originally blued with the 16-inch blade itself left bright, though some originals had blued blades. The M1 bayonet was parkerized from the git-go and had a 10-inch blade.
The "UC" on your bayonet stands for Utica Cutlery, which made many of these during WWII. I'd guess yours was made in 1943 or later, most likely 1944 or '45. Some of the 1943 blades have the year of manufacture stamped on the blade, but not all. The blade-dated bayonets are of considerable interest to collectors.
The M3 scabbard was originally made to fit the 16-inch M1905 blade, and many were cut down to fit the later 10-inch M1. The purpose-built 10-inch scabbard was the M7. The body of the M3 and M7 scabbards was most often fiberglass, the throat and belt hanger being parkerized steel. On a scabbard that's been around the block a time or two, it's not unusual to see the metal parts painted over with OD green paint. It's not original or correct, though.
The scales of your bayonet are made of bakelite, an early form of plastic. Most often, these are black like yours, though some reddish-brown ones were made early in WWII. The red ones are somewhat rare. The old M1905s originally came with wood scales, though many were rebuilt later with bakelite scales and a parkerized finish.
Also, some new production M1905s were made early in WWII. Collectors sometimes call these M1905/1942 or some variation thereof. They retain the 16-inch blade of the original M1905, but came with bakelite scales, parkerized finish, and generally lower level of fit and finish than the pre-war M1905s. The pre-war M1905s typically were serial numbered on the blade, whereas the M1905/1942s were not.
During WWII, the 16-inch blade was dropped in favor of the 10-inch blade. The shorter blade required less steel to make, was less likely to break in service, weighed less, and was handier for the soldier. Many 16-inchers were cut down to 10 inches, with a variety of point shapes. These are easy to identify in that the fuller ("blood groove") runs all the way to the tip, whereas a purpose-built M1's fuller stops a couple inches back from the tip. Collectors today often call the cut-down M1905s "M1905E1s"; however, back in the day, the military made no distinction between M1s and cut-down M1905s, simply calling them all M1s.
So anyway, you have a WWII bayonet there for the M1 rifle. It was originally made with the 10-inch blade, though your scabbard is a cut-down. Many, many of them were made just like it, so it doesn't have huge collector value, but it's still a bona fide artifact from WWII. Was it me, I wouldn't dig any more weeds with it.
Hope this helps, and Semper Fi.
Ron H.