Two different rifles.
This is the rifle Carson gifted to the Masonic Lodge in Monterrey NM. It was in Taos but now resides in Santa Fe. This rifle, if my memory is correct is 53 caliber and has a 31 inch barrel. I seem to recall it was the last Hawken Carson owned. The medallion reads "Presented to Montezuma Lodge (Lodge numbers) by Brother Kit Carson May 1868"