Compare 2 ranges with countifs

Thank you Quang,
I attached a sample excel to my original post.
I tried the formula you wrote, it gives me the total number of hits. I would need something that counts the number of rows where there is a positive hit.
So if there are 25 hits but it is only distributed into 6 rows, then I would need a formula that returns 6.

Try

=SUMPRODUCT(--(MMULT(TRANSPOSE(COUNTIF(Sheet2!$B$1:$H$1,Sheet1!$A$1:$Z$100)),ROW(1:100)^0)>0))

confirm with Ctrl+Shift+Enter

Thanks John, almost there, this gives actually a lower number of rows back as the numbers actually occur in. This formula misses some occurrences.
I do not know where the problem lies though. One thing I can think of is that when I set my cursor to ROW(1:100) it will highlight the rows on sheet2 instead of sheet 1.

After some more reading and playing around, finally found it!

=SUM(--(MMULT(--(COUNTIF(Sheet2!B1:H1,Sheet1!$A$1:$Z$100)),TRANSPOSE(COLUMN(Sheet1!$A$1:$Z$100)^0))>=1))

Thanks for all the hints.