The British used the following definitions for these -
1) Main line - The busiest route and the one generating the most amount of traffic.
2) Chord line - The shortest route, with lesser traffic than the main line, used mainly for long distance traffic without much traffic to intermediate places.
3) Loop line - Usually just an alternate route that is neither the...
more... shortest, nor the busiest.
For example, the original route from HWH to Delhi was via Jamalpur, now called the Sahibgunj loop. The first trains from HWH to Delhi went through this line for about 5 years. Then the line between Sitarampur and Kiul was constructed. Initially the main traffic was still via Jamalpur so, the new line was called the 'Sitarampur Chord'. Shortly afterwards, more traffic started going through Sitarampur, so it became the main line, while the line via Jamalpur became the loop line.
The Grand Chord came up almost 35 years later. Until the 1960's, there wasn't much traffic on the Grand chord, so it never became the main line. Had the Britishers still been present, they would have termed the Grand Chord as the main line and the line via Patna as the loop line.
Same with the LKO-BSB route. LKO-FD-BSB came up in the 1870's and was the main line. The route via PBH came up in 20 years later in 1898 and soon became the main line, while the FD line became the loop. The line via SLN being the shortest, is termed as the chord.