Charles, if you are able to get a hold of a volume titled: THE ARMY'S NAVY SERIES: DICTIONARY OF TRANSPORTS AND COMBATANT VESSELS, STEAM AND SAIL, EMPLOYED BY THE UNION ARMY, 1861 - 1868, compiled by Charles Dana Gibson and E. Kay Gibson, published in 1995, you will note that the vessels in your reference (Report on the battle of South Mills, April, 1862) are all definitely non Naval steamers, that were used by the army as transport vessels. I checked my copy of the volume, and yes indeed, there was a steamer also named the MASSASOIT, and the data given is as follows: "Chartered March 5, 1862 - November 25, 1863. Transported troops who carried out a raid up the Pasquotank River in April 1862. Chartered November 26, 1863 - May 30, 1865. Aided in the evacuation of noncombatants at the time of a Confederate raid on Plymouth, North Carolina, in April of 1864. On a raid up Chowan River, North Carolina, during July of 1864. One of 99 vessels engaged in the supply of Sherman's army after it reached the sea at Savannah, Georgia, in December of 1864, and later during the Carolina campaign of early 1865."
The Gibson volume does also have entries on several steamers named VIRGINIA, as well as one on the PHOENIX, and three on the OCEAN WAVE, although the one referred to in your reference was a sidewheel steamer of 270 tons, which is also indicated to have been used to carry troops for the raid up the Pasquotank River in April, 1862. Also mentioned in the volume are the sidewheel steamers NORTHERNER and GUIDE. So there is no doubt that all the vessels mentioned in the report were not vessels of the United States Navy, but steamers in service of the army.