The 13th New York Infantry Regiment is a different organization.

In April of 1862 legislation changed the designation of militia units to “National Guard.”

1861
April 21 Organized for service under Colonel Abel Smith
April 23 Eight companies (486 men) mustered into United States service for three months and sailed in the steamship Marion to Annapolis
April-May Guard railroad at Annapolis, Maryland, quartered in the buildings of the Naval Academy and assigned to the Department of Annapolis.
May 7 Additional reinforcements raised the regiment’s strength to 793 men.
May 18 Affair at Smith’s Point, Md.
June 19 Moved to Baltimore, Md.
July 21 The regiment agrees to General Dix’s request to extend its service by ten days
August 6 Mustered out of United States Service at Brooklyn, having lost 5 men to disease. Many of the regiment enlisted in the 87th New York Infantry.
1862
May 26 Ordered to Washington D.C.
May 28 Mustered in for three months United States Service
May 30 Left for Washington under Colonel Robert B. Clark
June-
September
Served at Suffolk, Virginia as part of the 7th Army corps
September 12 Mustered out of United States Service at Brooklyn, having lost 1 man to disease and 1 killed in an accident
1863
June 18 Orderd to Harrisburg under Colonel John B. Woodward
June 20 Mustered in for three months United States Service and attached to 2nd Brigade, 1st Division, Department Susquehanna
July 2 Engagement near Fort Washington, Pa.
July 21 Mustered out of United States Service at Brooklyn, having lost 1 man to disease