A leisure battery is like a car a battery, but designed for a long, slow load draw, not a quick, deep charge (like starting a car). It can run things that are 12v, but doesn’t have any plugs, so it need to be wired up to things, such as in a campervan, both to recharge and to charge other things. It WILL NOT heat anything. Not enough oomph. It will charge phones and low wattage appliances. (If it or heats it cools, it’s a nope!). You can power 240v (ie normal plug) if you use an inverter to concentrate the power, but you will use is very fast. Sure, you can power a radiator. For four minutes! But you can charge a laptop, and possibly a router. (I’m not sure how hungry they are. I can’t imagine that much)
a ‘power station’ ie jackery, power oak or eco flow. Is a bigger, better battery with all the plugs and inverter thingummies inside. Its basically a big power bank. It’s plug and play, up to a point. You plug it into a power source to charge up (don’t need an electrician or crocodile clips) and it has (usually) all kinds of usb, 12v abd 3 pin sockets so you just plug stuff in. THERE ARE DIFFERENT MODELS AND THEY POWER DIFFERENT THINGS AT DIFFERENT PRICE POINTS.
The Ecoflow delta mac is around £2000. It’s ‘top of the middle’ of the range. Will power pretty much anything. Not for long, but most things will work. (I reckon an American ff or tumble dryer would struggle, but would drain it in minutes anyway). Again, forget heating, except maybe a heated throw (get something safe and gas powered. It’ll be cheaper). A microwave, induction hob, hairdryer. All fine, but only for maybe 30 minutes (and not at the same time). The router will be good. It might do a ff for a few hours. The Rivers are a bit smaller and cheaper and great for CPAP, coffee makers, laptops etc. probably a router (I need to check) but no induction, microwave or hairdryer for sure.
I don’t know anything about UPS, but I think they are just versions of the power bank wired into your home, or part of your home that kick in automatically if your power goes out. Happy to be corrected. Bet they don’t heat anything either. Broadly speaking, you can’t heat or cool on a battery in any practical way.