Help! What is this? 2016 BMW 528i

2016 bmw 528i

Heater , coolant, radiator, water hose? I see so many different things as I research. Car is no longer holding coolant , it immediately leaks when added; and when idle begins to smoke from disconnected hose. Please help ASAP! Looking for someone to do the work but I’d like to have an idea of the sort so that I can purchase on my own to minimize costs and being overcharged for parts + labor. I have attached a photo of the disconnected /blown hose alongside a photo of the hose I’m looking to buy. What is the part that’s broken and is the screenshotted ítem the same?