Detect new values when comparing existing variables in a dataframe and add them in a new variable in R

I would like to create a new column with the values that are in col1 and not in col2:

And what if the separator is a || instead of a ,?

Loop rows, split, get the set difference, finally paste them back together again:

d$col3 <- apply(d, 1, function(i) {
  paste(setdiff(unlist(strsplit(i[ 1 ], ",")),
                unlist(strsplit(i[ 2 ], ","))), collapse = ",")})

d
#                  col1       col2         col3
# 1  First,Second,Other  row,First Second,Other
# 2 Second,Other,Other2 row,Second Other,Other2

If we want to split on "||" then apply below changes for strsplit in above code:

#example for ||
strsplit("First||Second||Other", split = "||", fixed = TRUE)
# [[1]]
# [1] "First"  "Second" "Other"