J.C. Higgins is a line of sporting goods offered by Sears from 1908 to 1961, when the line was renamed Ted Williams after the famous baseball player. They were made under contract by a lot of different gun manufacturers, namely High Standard, Winchester and Marlin that I know of, and probably many others. I think your model 44 is made by Marlin and is similar to their model 57, but that's just a guess on my part.
My family has owned several "Sears" brand guns over the years, and we still use most of them.