You can use strsplit and intersect from the base
library:
> a <- "Roy lives in Japan and travels to Africa"
> b <- "Roy travels Africa with this wife"
> a_split <- unlist(strsplit(a, sep=" "))
> b_split <- unlist(strsplit(b, sep=" "))
> length(intersect(a_split, b_split))
[1] 3