bash: $0 value

When a script is run from a command line then the 0th parameter is the script's name. However, when a script is run via source command, then the 0th parameter is a shell name. Weird, but true.

$ cat test.sh 
echo "\$0 is $0"

$ bash test.sh
$0 is test.sh

$ source ./test.sh
$0 is bash