Current State:

Currently the widget and help center request type search retrieves different results as they use different API endpoints to search for request types.
The widget search should return less options as it uses the following endpoint:

• Get request types

And according to the page, the search brings values based on the following statement:

searchQuery which is matched against request types' name or description. For example, the strings "Install", "Inst", "Equi", or "Equipment" will match a request type with the name "Equipment Installation Request".

Proposed Future State:

Use the same search mechanism across widget and help center request type searches so they retrieve the same values.