There are various ways to look up info. Here's one.

I would probably have the reconciliation sheet show both numbers so I
can see the difference when necessary. So say Col A is the vendor name
and B is the reference to the first sheet, C to 2nd sheet, D = B minus
C.

This can go in B2 and copy down (you'll have to modify to your sheet
names and ranges):
=SUMIF(Sheet1!$A$2:$A$1000,A2,Sheet1!$B$2:$B$1000)

It would be easier to do the second sheet if it had the vendor names
on every line like the first one. Or if the Subtotal description
included the vendor name, you could have Excel search on that. I think
there is a way to find the vendor, then skip down to the first row
after that with "Subtotal" in it, and return that amount, but I don't
know how offhand. Much easier if you could change it just a bit.

Also, generally speaking, you need to make sure there aren't errors or
typos in the vendor names anywhere. Otherwise a lookup can miss
something. Sometimes you can get around that with wildcard characters,
but if you have vendors with very similar names (often cities or
states in the name), wildcards can be more of a problem than a help.