SmithCart product search treats multiple words as one search term and uses like '%word1 word2%'.
I'm not quite sure why HP 3000 works, perhaps the search is different from the Products admin page.
This brings up two issues. On the admin product search, the selected search method should be persistent. I know I always search by SKU and need to select the dropdown each time. A more deeper problem is the simplifed single search term in products search. I think should be modified to include multiple words for inclusion as well as exculsions.
For example, I find it confusing when
10 finds 100, 1000 or anything with '10'
'red' will find red, ordered, centered, coloured, credit, predelivery, credenza (not quite what I was looking for)
'red dress' currently finds 'red dress' but will not find 'dress' and 'red'
Or if I want not want a red dress, I would like to use 'dress -red'
Using ling this would be easy, using the DNN DAL is a little more difficult, but it can be done.