Conditional formatting question

As per your example, Assuming range A1:A10 has numbers from 1 to 10. Now select B1:B10 and make new rule using the below formulas

For green

=ISNUMBER(MATCH(B1,$A$1:$A$10,0))

For red

=AND(B1<>"",ISERROR(MATCH(B1,$A$1:$A$10,0)))

Find the attached sheet to see if this is what you are trying to do and if its not, please upload a sample workbook with desired output.