Not uncommon that in the earlier period of the war one could sign up (enlist), then it could be a couple weeks or months before the respective unit is called to be formed up once enough names/enlistments are had to fill it. Especially in rural areas.
He may have enlisted (signed up) on June 25th 1861, but they didnt have enough numbers to fill till July 31st 1861, when the respective unit was "formed" or "enrolled", which may be in another place than where one may have originially signed up at. And/or date/location of where it might have physically been when it was reorganized. 8th Va Cav Regt Company-D was formed up on July 31st 1861.
Some units may have been formed initially intended for one year duty or more, This might be different from what some members individually signed up for. Not totally uncommon to find folks in one unit that have different enlistment terms, or different than what the company or regiment itself committed for. If majority in a given unit only enlisted for one year.. at the end of that term if not enough re-enlisted, the unit itself might be disbanded or reorganized. If it is sent home those within that still have service obligations of longer terms, they usually are transfered to other existing commands. If they have enough to stay in the field they usually replace the expired enlisted people with new recruits.
"Princeton Sept 20 1861" This was where the unit physically was when their monthly muster roll return was done. The one year reference is what the unit originally mustered for, which may or may not reflect the terms of all those within the unit. Companies held roll call usually at least twice a day. Each month a formal complete muster roll is done and turned in up the chain of command. On the "cards" it is typical that they combined several months worth of monthly returns notated on a single record card.
Frederick
(Richmond Va)
PS just curious what area of the country are you located? Ohio?