Difference betwen "Add Assignment" and "Assign to me"

Hi,

Troubleshooting mail notification I found difference betwen two methods od assignment.

As showed on image - Assign to me (incident 27) is filling "Current assigned analyst" "current assigned group", "current assignment user" and "current assignment group"

"Add assignment" (incident 25) is filling "Current assigned analyst" only,

For comparision incident 26 is just created by Self service user.

Booth - "Assign to me" and "Add assignment " from process point of view looks similar, and uses same window, but why is that difference? As a result of this some notifications works - if Analyst clicked Assign to me, and some not...