Stainless steel is definitely safer than plastic in any temperature condition. Even those plastic without BPA, which are now being replaced with BPS / BPF, those 2 compounds still have many similarities with BPA. Apart from that, the characteristic of plastic doesn't change, meaning it will continue to leach some plastic into the water at warmer temperature.

Be aware that there are some stainless steel container that are actually aluminum, and those have plastic coating on the inside. So pouring warm/hot water inside will results in leaching of plastic content into the water.

Paper cups usually have a plastic coating on the inside. That's how it stays waterproof for so long. And those plastic coating will leaches into the drink.

Usually if they mentione stainless steel, then it is stainless steel.

Aluminium, maybe you can feel it's light, but then it's hard to judge unless the bottle is naked.