It makes me laugh how we all use different words for the same things. I always called those “drainers” dish or drying racks. I only pull one out when I am doing a lot of hand washing. Otherwise I keep a kitchen towel to place them on, and once they dry, I toss the towel in the laundry.
“Drainers” to me (and I very well could have made this up in my mind as I have a tendacy to misuse works to suit me) are those catch alls in the sink that fill up with junk that makes me gag.