What do you call the segment of track between two train stops?

There are a number of terms used within the railway industry to define sections of track infrastructure where conventional signalling is used.

Technically, a Track Section (sometimes Track Circuit) is the piece of track between two signals, not between two stations.
A Berth is a location within which a single train may be located. This is usually a group of track sections.

The section of track between two stations is known as a Path. This will encompass a number of Berths and will also define the running line (e.g. fast or slow) as appropriate.

Train timetablers (British English) or schedulers (American English) will create the train's timetable/schedule by defining its paths.

In the example you give, a path would be the term most understood in the industry.

One of the best sources of explanation for railway technical jargon is here.

Although I don't think this is a word used in the railroad industry, I'd be tempted to call uninterrupted track between two stations a segment.

No. The "station" is the passenger platform, or a building that houses or is adjacent to one or more of those platforms. The track that runs between stations is a section or length of track. The entire length of track between two endpoints is often called a "line".

I would call it a stretch. The Free Dictionary gives this definition:

n. 3. A continuous or unbroken length, area, or expanse: an empty stretch of highway.