The "Recipe" search searches the text of all the recipes of the selected cookbooks. For example, if you search for "tomato", it will return also the recipes that require tomato sauce and tomato cans, not just fresh tomatoes. The "Ingredient" search looks for recipes that have an ingredient linked to the specified grocery item. The search is independent on the exact wording or spelling of the ingredient in the recipe, as long as it is linked to the appropriate item.
To use the ingredient search, type at least the three first letters of the ingredient and click on the arrow of the pull down menu. You should see a selection of grocery items. Select the one you want. Before proceeding with the search, make sure that the color of the ingredient has turned black.