Destination initiated handshaking vs source initiated handshaking in asynchronous data transfer-:

In destination initiated handshaking-:
1) Disable ready for data
2) Disable data valid

That means first destination says "I received data totally". Then source stops sending data.

In source initiated handshaking-:
1) Disable data valid
2) Disable data accepted.

That means first source stops sending data, then destination says "I have received data totally"

Source-: https://cvbl.iiita.ac.in/sks/coa-files/lectures/Lec_11_IO[1].pdf

Why are these 2 different order from each other?

It's dependant on which side is the "master":

As an analogy..
eg. Receiver is master:
"Throw me another ball"; "OK, I've thrown one".

Or, sender is master:
"I'm throwing you another ball"; "OK, I got that one".

The two communications reverse order between the two arrangements.