Their free box swap campaign that you see on the ads, is currently targeted to all PVR box customers because the On Demand service on PVR box will discontinue on 31 Dec.
But if your boxes are not PVR box, then there will be another set of T&C applies.
Most importantly, your Astro monthly fee subscription must be RM60 and above to qualify for free box swap.

Wonder if there is any change of satellite dishes for the swap.
Why? Is your current dish badly damaged or what? Cuz otherwise there's no need to change new dish one.

In fact, by default, they will create your box swap order as a Plug & Play, meaning your new box will only work properly on Plug & Play mode, which means 100% internet streaming only and does not rely on satellite receiption.
When that happens, your current satellite dish will be left unused and abandoned on your rooftop.

If you insist wanting to continue receiving Astro channels via satellite, then you must explicitly mention to that agent that you want it to be in Satellite and not Plug & Play.
Otherwise, the default will be Plug & Play.

I think there's one that's a mix of both satellite as well as plug & play

I believe you're referring to the Continuous Viewing feature, where if your Ulti/Ultra Box is on satellite mode, a pop-up appears prompting you to switch to Internet streaming during heavy rain so that you can temporarily continue watching the TV channel.

This feature only available when the Ulti/Ultra Box is on satellite mode and it is connected to the Internet.
If the box is not connected to Internet, then this feature will not work.

You can call it a "hybrid", but from system's perspective, it is still considered Satellite.
It is different than Plug & Play mode, which does not use and completely ignore satellite dish reception. It fully relies on Internet streaming only.