Hello Joyce,

These are two distinct units:
The 2nd Arkansas Cherokee Mounted Rifles were active in the Trans Mississippi Theater.
http://members.aol.com/ciiisiii/cherokeepage/indcsaunits.htm

Both the 1st and 2nd Arkansas Mounted Rifles went east and became part of McNairs Infantry Brigade (later Reynolds Brigade) from April 1862 until the war's end. The book "Rebels Valiant" is about this unit.
http://www.couchgenweb.com/civilwar/2ndmtf&s.html

I would suggest looking page the Arkansas History page for further info.
http://www.history-sites.com/mb/cw/arcwmb/