Searching Within Search Results?

Is this limiting the search to when the verse reference appears within the section under the heading/large text/title? Or is this searching the whole resource for the heading to include the word Law, then the verse reference separately regardless of whether it's in the section under the heading?

Basic searches always operate within the context of a single "article". Unfortunately, the exact bounds of an article are not always consistently defined from one resource to the next and are not always exactly what you might want.

You might find a heading in the middle of an article. You could work around this by using the BEFORE operator instead of AND. This would ensure that the text in the heading is found in the text before the reference.

You can get a sense of article boundaries using the Article navigation option in the Locator bar for the resource (if not visible, use the panel menu to display it).

You may also find a top level heading in a different article than some of the content of the text belonging to that heading (such as when a long section of text has multiple subsections). In this situation, your search may not be able to find any results because the heading and reference might not be in the same resource article. Unfortunately, there isn't really a workaround for this.

As a follow up question, what is the difference between searching as discussed so far vs. <1 Timothy 1> INTERSECTS {Headword Law}. I'm getting very different results and trying to understand what determines Headword in a resource.

A headword is what's called a milestone, which is a section of a book that has been tagged in an index by Faithlife. Milestones can also be references, such as the Bible references in a Bible or commentary. Just like with a Bible reference milestone, you can navigate to a specific location in a book using a headword by typing in the navigation box at the top of the resource panel.

You commonly see headwords used in dictionary, lexicon, and encyclopedia type resources to allow you to navigate to a specific entry in the book. You can tell a resource uses headwords by checking the Indexes section of the information page on the resource. There it will indicate that headwords are present in a specific language.

Headwords don't have any formal consistency, which means that there is no guarantee of a consistent term that might be used to capture a single concept across all resources (although lexicons and dictionaries are generally much more consistent than encyclopedias). However, you can see the headword at a location in the resource by right clicking in the text.

Headwords have the benefit that they accurately mark (excepting a tagging error) the boundaries of a block of text about a subject.

The search you get from Factbook includes headwords, and often multiple headwords (based on alternate titles) in an attempt to catch as many articles about a subject as possible, but it is still no guarantee to find them all given the inconsistencies in naming.

And Is there a way to do a Headword search without having the exact headword?

There is not.