Most commercial flights are likely to be following the published instrument approach procedure for that destination. These are set by the authorities responsible for regulation of aviation in that country. No doubt it is possible to link to the approach plates for the airport in question.
Depending on the standard of equipment on each aircraft and the navigation aids used to assist with the approach (ie, a precision versus non-precision approach), the path over the ground taken by each aircraft can be quite different. Given that instrument approaches follow bearings and distances based on transmissions from radio beacons, even 'accurate' approaches can appear to follow quite markedly different courses over the ground to a ground-based observer.
Also, some operators may request and be granted permission for a visual approach by the local ATC unit. In this case, the path followed may be very different to an instrument approach, and each visual approach may be different to the previous one due to ATC instructions for aircraft separation.