In R what is the difference between message and sink to stderr - r

Question

This question is inspired by this post where printouts from a called functions are displayed inside a shiny app when the code is running.
My question is basically, what is the difference between:
message('hello')
#and
sink(file=stderr())
cat('hello')
In the documentation for message it says that:
The default handler sends the message to the stderr() connection.
I haven't found a way to illustrate the difference in just R without shiny , but in this example the 2 functions behave differently
library(shiny)
library(shinyjs)
myPeriodicFunction1 <- function(){
for(i in 1:5){
msg <- paste(sprintf("[1] Step %d done.... \n",i))
message(msg)
Sys.sleep(1)
}
}
myPeriodicFunction2 <- function(){
for(i in 1:5){
msg <- paste(sprintf("[2] Step %d done.... \n",i))
cat(msg)
Sys.sleep(1)
}
}
runApp(shinyApp(
ui = fluidPage(
shinyjs::useShinyjs(),
actionButton("btn1","Message"),
actionButton("btn2","Sink to stderr"),
textOutput("text")
),
server = function(input,output, session) {
observeEvent(input$btn1, {
withCallingHandlers({
shinyjs::text("text", "")
myPeriodicFunction1()
},
message = function(m) {
shinyjs::text(id = "text", text = m$message, add = FALSE)
})
})
observeEvent(input$btn2, {
withCallingHandlers({
shinyjs::text("text", "")
sink(file=stderr())
myPeriodicFunction2()
sink()
},
message = function(m) {
shinyjs::text(id = "text", text = m$message, add = FALSE)
})
})
}
))
Can anyone help me straighten this out?