IIR, the Ballard 38-50 was an "everlasting" case. The 38-55 Ballard evolved from it with a more modern drawn case.
COTW,3d Ed. says The external dimensions were the same, except for 1/10th in.* greater length. Marlin took over Ballard in 1881, the 38-50 dates from 1876 but was a handloading only proposition. The change to the 38-55 occurred in 1884 with the Union Hill No. 8 & 9.
*. In the dimension chart Frank Barnes shows 2.00 for the 38-50 and 2.1295 for the 38-55.