So many possibilities
I think you can't give all cards the same way, it will depends on the foul committed, how the game is going etc..
If I want to have a quick word with the player, i'll take him apart, speak and show the caution, however, sometimes you just have to show the card after blowing the whistle. The important thing is that it's clear for all players, staff and spectators which player you've cautioned, so if the foul was clearly made by one player, no need to take him apart if it's not to have a word.
And some other time, mainly in red situations, you want to show everybody that you saw what you saw and the red is coming, for a really gross SFP for example, I would take the red out of my pocket as soon as possible, it defuses the tension of the time where players will be wondering if you're going to show red or not, start to argue, get mad at each other etc..