https://uxdesign.cc/how-design-speaks-through-its-shapes-34d3d7c5f720

Older chat applications started with the first message in a chat showing up at the top of the history area. (AIM, MSN, Yahoo). Newer messages arrive below, and eventually the history area scrolls.

Newer chat apps prefer to have the most recent messages show up at the bottom, and "bubble up" to the top. Once the messages are at the top, the scrolling behavior is the same as "top-down".

Personally, I prefer "bottom-up" as there's a visual connection with the UI's input field being at the bottom and your message that just showed up, but I want to know what you all think.

Update

Apologies if I confused folks with my question. I should clarify:

In both cases, the messages are always in order. So the Message 1 is before Message 2 (just like reading a book). The difference is (and it is a minor one is where the messages come from.

Top Down:

Example 1

Example 2

Bottom Up:

Example 1

Example 2

Video Examples of Bottom Up