Upvote:1
If you book the first - cheaper - version, you have two independant tickets, and it is your problem to make the connection. If your arriving flight is late - for whatever reason - you lose the second ticket, and will be stranded (and have to buy a new one, typically no refunds).
Emirates (and most others) do normally not easily offer such separate bookings, to avoid angry customers that don't understand what they do, and because they prefer to sell the higher priced ticket.
Also, booking separate tickets means your luggage does not get checked through - you need to leave the secure area, pick up your luggage, and check-in again. This takes significant time, and potentially requries a visa (!), a COVID test, and/or other things, as you are entering the country - doesn't matter that you plan to leave again right away. Consider it as you are immigrating into that country - for half an hour.
Looking at your times, you will for sure NOT be able to connect in PTY in the short time if you have separate tickets - you need to take a later flight for the last leg.
That being said, if you are sure you can manage / avoid the visa issue, and have enough time between flights, you can save the money and book two tickets. It might be a good plan to leave a day inbetween, or be ready to buy a second ticket for the connection (still cheaper...).
I have done such splits often, and it always worked, but sometimes it got really tight; it is not for the faint of heart. Still saves a lot.
Flight changes: it depends on your ticket class. Probably not for free, but it's guesswork without seeing the details.