Incomplete Search Result in Admin

[Stenrique]

Are these:
products_name
products_model

They, "NBS-10*" (where * is a wildcard), are products_model.

what are the fields that contain this information?

It's the Model col. in admin->Catalog->Categories/Product

How many do you see on the page when you enter:
NBS-10

There were only 3 items shown. However, when I key in the same search term at the online storefront, 4 items were shown.

Is there perhaps another page to navigate to on the search?

Are you referring to the search in admin or storefront? On the admin side, the search result is shown in individual rows (I'm sure you know that, I'm merely adding this for completeness sake ) while on the storefront, these products are spread across 3 separate sub-categories.