From the Sunset Western Garden Book (1996) (p. 495), under the "Strawberry" heading:
"'Fort Laramie' Everbearing. Good yield of large, bright red berries over long season. Excellent flavor.
"'Quinault. Everbearing. Fruit is large, attractive, tasty, rather soft. Good producer of runners."
From this, it sounds as if the plant with the "many runners" is the Quinault, and the other one is the Fort Laramie.
-- dkra