In the NYC Subway terminology, a "line" means the physical trackage used by trains that are used by lettered or numbered services. Currently, the company or division names are not used publicly, when the line names may be used occasionally. The services that are running on certain lines tend to change periodically, but the lines refer to static trackage.
Therefore the line represents the physical structure of tracks that trains run over. Every section of the system is assigned with a unique name that necessarily starts with its first division (IND, IRT, or BMT). For example, the line that runs under Eighth Avenue is called the IND Eighth Avenue Line. During the time, some lines have changed their names and divisions, but this happened relatively rarely.
Service in the subway terminology refers to the route which the train takes across the various lines. A service can operate along various lines and even different divisions. For example, the R service is running along the IND Queens Boulevard Line.
Currently, the New York City Subway includes 36 different rail lines. The 63rd Street Lines and the Archer Avenue Lines are both classified as two separate lines because of their structure. Both lines are available to serve two divisions on distinct sections of track.
Each line has a specific color and name. For example, the 8th Avenue line is always blue when Broadway 7th Avenue is always red. Due to the number of lines, even locals frequently don't know the official name of the line.
However, even though it might be tempting to use the color system to describe directions, single letter/number designation for the specific services is still necessary. It will be confusing to say that someone is taking the "blue" 8th Avenue line because included three services go to entirely different locations and even stop at various stations on the same shared path. Due to that reason, locals never refer to lines by their colors or names. Despite having different meanings in NYC subway vocabulary, the word "line" is usually sometimes used instead of train or service.
The longest line is the 8th Avenue "A" Express train, which stretches more than 32 miles, from the far southeast corner of Queens to the northern tip of Manhattan.