Spot on. I hunt red deer and while you _can_ use .223 / 5.56mm, a humane kill requires very precise shot placement. It's okay for smaller deer (fallow, whitetail, sika) and chamois, but not really for the reds, sambar, rusa or tahr.

I use .308 Win, probably the most common calibre for red deer hunting here, but you meet people using fancy powerful rounds like 7mm Rem Mag or .338 Lapua.