I think I have had this problem before between these two names. Bronson lace vs. Swedish lace!!
The kit I have is for the Lickety-Split Bathmat. (Yarn Barn-KS). The yarn is 16/8 Heavy Cotton. After some research, I found this draft information in New Key To Weaving by Mary Black:
The kit's draft is presented like the bottom example but tells me it is Bronson Lace. Mary Black says in her book on page 317:"Actually, there is so little difference between the finished appearance of Swedish lace and Bronson lace that weavers are at a loss to differentiate them."
Since, according to Mary, I am threading the loom to Swedish lace, I will call it that in my head. I might even call it that when I get it woven off and have it laying on the bathroom floor.