A pure bash answer

 echo "0 hello world the man is world
 1 this is the world
 2 a different man is the possible one" | while IFS=$'\n' read -r line; do echo $line | tr ' ' '\n' | sort -u; done | sort | uniq -c
 
 
 1 0
 1 1
 1 2
 1 a
 1 different
 1 hello
 3 is
 2 man
 1 one
 1 possible
 3 the
 1 this
 2 world

I looped unique words on each line and passed it to `uniq -c`

edit: I did not see glenn's answer. I found it strange to not see a bash answer