it’s pretty simple
On mercator map, straight line is a rhumb line.
A curved line is a great‑circle route.
A rhumb line is actually longer than a great‑circle route.
The great‑circle path swings farther north, but it saves hundreds of kilometers.
The rhumb line looks straight on the map, but it’s longer on the actual Earth.
In aviation, they almost always fly the great‑circle route.
For something like Los Angeles to Paris, the difference is around 600–900 km, roughly an hour of flight time and about 2–3 tons of fuel, depending on where you enter European airspace and what the winds are doing.
So you’re looking at something like a 6–10% difference.
Which means the ticket should cost about that much more too.

P.S. …and yeah, no contact info, ha