subtract value from previous row by group

With dplyr:

library(dplyr)

data %>%
    group_by(id) %>%
    arrange(date) %>%
    mutate(diff = value - lag(value, default = first(value)))

For clarity you can arrange by date and grouping column (as per comment by lawyer)

data %>%
    group_by(id) %>%
    arrange(date, .by_group = TRUE) %>%
    mutate(diff = value - lag(value, default = first(value)))

or lag with order_by:

data %>%
    group_by(id) %>%
    mutate(diff = value - lag(value, default = first(value), order_by = date))

With data.table:

library(data.table)

dt <- as.data.table(data)
setkey(dt, id, date)
dt[, diff := value - shift(value, fill = first(value)), by = id]

You can do this with the ave function:

data$diff <- ave(data$value, data$id, FUN=function(x) c(0, diff(x)))
data
#       id                date value diff
# 1   2380 2012-10-30 00:15:51 21.01 0.00
# 2   2380 2012-10-31 00:31:03 22.04 1.03
# 3   2380 2012-11-01 00:16:02 22.65 0.61
# 4   2380 2012-11-02 00:15:32 23.11 0.46
# 5  20100 2012-10-30 00:15:38 35.21 0.00
# 6  20100 2012-10-31 00:15:48 37.07 1.86
# 7  20100 2012-11-01 00:15:49 38.17 1.10
# 8  20100 2012-11-02 00:15:19 38.97 0.80
# 9  20103 2012-10-30 10:27:34 57.98 0.00
# 10 20103 2012-10-31 12:24:42 60.83 2.85

The first argument is the data to be operated on, the second argument is the group, and the last argument is the function to be applied to the data from each group.