This is not as expensive as you probably think. Assume

Compaq Presario Laptop Model No P440 L100 Series (PSLA0L-00U00E)
[download]

... as input ->

00
440
100
Compaq
Laptop
Model
No
Presario
Series
PSLA
[download]

Then we need todo something like this:

...
# get vendor id:
SELECT id FROM vendor WHERE NAME=00 or NAME=440 ...

# check all words
foreach (@word) {
  SELECT product_id FROM words WHERE vendor_id=? and word=?
  for my $id (@ids)
    $cnt{$id}++
  }
}
[download]

How you then analyze this match statistic depends on the data. But the editdistance is probably the wrong metric, you are right.