The last time I had to use Move To iOS it just copied everything. „Transferring“ is copying with an extra step of deleting the original data, in this context. That could potentially mean to lose data, which is why it should still just copy everything.

WhatsApp was another story, back then there was no official way of transferring your messages. It is possible now, but keep in mind that you can only have one device per WA account, as it is tied to your phone number/sim. There are third party solutions(like WA browser) which connect to your main account, no official way of having the WhatsApp app twice using one account though.