Appears to be the same individual:

Benjamin F. Thompson, Private, Company H, 22nd Texas Cavalry, enlisted May 1, 1862 at Fort McCullock, 27 year old Farmer, born in Missouri, sandy hair, blue eyes, fair complexion, 5’ 10”, promoted 2nd Sergeant August 1,1862, reduced September 30, 1862, recorded March 1, 1863 as absent, sick, discharged for disability May 7, 1863, Clarksville, Tx.

Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Texas
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Benjamin F. Thompson, 2nd Lieutenant, Captain Thomas F. Whaley’s Company, 1st Frontier Frontier District, Major William Whaley, Commanding, TST, enlisted January 1864 at Gainesville, Texas, mustered in March 1, 1864 at Gainesville, discharged after 30 days service, age 29 years

Texas, Muster Roll Index Cards, 1838-1900

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1860 United States Federal Census

Name: B F Thompson
Age: 25
Birth Year: abt 1835
Gender: Male
Birth Place: Missouri
Home in 1860: Cooke, Texas
Post Office: Gainesville
Family Number: 288
Value of real estate: 1200/245
Household Members:
Name Age
B F Thompson 25 Farmer
Melvina Thompson 24
George F Thompson