All three are sheep’s wool; the difference is the fibre and how tightly it is knitted (sample guide).
Merino is fine and smooth, warm without bulk, and sits under a jacket. Lambswool is softer and a little thicker, the everyday crew neck. Shetland is springy, a little scratchy at first, and keeps out the wind for twenty winters.
Wash any of them cold, by hand or on the wool cycle, and dry them flat. Fold, never hang: a hanger stretches the shoulders in a week.