Lamar topped everybody with 11 nominations. Swift earned seven, as did producer-singer the Weeknd.
The nominees for album of the year are "1989" (Swift), "Beauty Behind the Madness" (the Weeknd), "To Pimp a Butterfly" (Lamar), "Sound + Color" (Alabama Shakes) and "Traveller" (Chris Stapleton).
The nominees for record of the year are "Blank Space" (Swift), "Uptown Funk!" (Mark Ronson featuring Bruno Mars), "Thinking Out Loud" (Ed Sheeran), "Can't Feel My Face" (the Weeknd) and "Really Love" (D'Angelo and the Vanguard).
The nominees for song of the year -- a songwriter's award -- are "Thinking Out Loud," "Blank Space," "Alright" (performed by Lamar), "Girl Crush" (performed by Little Big Town) and "See You Again" (performed by Wiz Khalifa featuring Charlie Puth).
The nominations were spread fairly evenly among films up for outstanding performance by a cast -- the SAG Awards' equivalent of Oscar's best picture -- with "Trumbo" earning three nods and "Spotlight," "The Big Short" and "Beasts of No Nation" picking up two each.
Also getting two nominations: "Room," "Steve Jobs," "Carol" and "The Danish Girl."
"Straight Outta Compton," the hit film about rap group N.W.A, received the fifth slot in the cast category, outdoing films such as "Joy," "Steve Jobs" and "The Martian."
The SAG Awards are considered one of the bellwethers of "awards season," when a number of groups hand out honors for the best films of the year. The Golden Globe nominations come out Thursday.
The NSFC also hailed Michael B. Jordan as the year's best actor for portraying the title role in "Creed," and Charlotte Rampling was tapped as best actress for her performance as a long-married wife in "45 Years."
Mark Rylance was named best supporting actor for "Bridge of Spies," while Kristen Stewart scored the best supporting actress nod for "Clouds of Sils Maria."
Best director honors went to Todd Haynes for his period romance Carol.
Fifty-three active members of the society took part in the organization's 50th annual voting meeting, held at the Film Society of Lincoln Center in New York City.
The Hollywood Reporter: Filmmakers Nailed 'Spotlight,' Says Boston Globe Editor
Best picture: Spotlight
Best actor: Michael B. Jordan, Creed
Best actress: Charlotte Rampling, 45 Years
Best supporting actor: Mark Rylance, Bridge of Spies