The different names are confusing. More so due to the legacy terms of mayor and minor service. All these terms in the automotive industry are used to describe different levels of maintenance or servicing for a vehicle. The specific tasks included in each type of service can vary between manufacturers and service providers, but generally, the following distinctions are observed:

Minor and major service stem from the time, vehicles required spark plugs and points to be changed every second or third service. The minor service included tasks like:
Oil and oil filter change.
Visual inspection of the vehicle components.
Check and top-up of fluid levels (coolant, brake fluid, power steering fluid, etc.).
Inspection of lights, wipers, and other basic components.
Tyre pressure check and adjustment.
Basic safety checks.

The Major Service would perform all the items in the minor service with the inclusion of:
Replacement of air filters and fuel filters
Replacement of spark plugs, points, and ignition system checks.
Comprehensive inspection of the braking and steering system.
Basically, the major service is more comprehensive and are often scheduled at specific mileage intervals or based on the vehicle's age.
Major and minor services belong in the past. Modern cars with spark plugs that last up to 120k and electronic ignition or engine management do not need the constant attention to these items.
"Logbook service" and "general service" are terms best used today. Sure some may call the General Service a “car maintenance service” or “essential service” to describe the service that is not a logbook service. The distinctions between them can vary based slightly on regional practices and specific service providers, but generally, they refer to the following:

Logbook Service:
Logbook services are scheduled maintenance tasks that adhere to the manufacturer's specifications outlined in the vehicle's logbook or owner's manual. The tasks to be performed are detailed in the Logbook, hence the name. Logbook services are designed to maintain the vehicle according to the manufacturer's guidelines, ensuring that it stays within warranty requirements and performs optimally throughout its lifespan. Following the logbook service schedule is crucial for maintaining warranty. This logbook specifies the distance and age of the vehicle for the service to be performed. For a logbook service it does not matter if the vehicle has travelled very little distance. If the 40k or 24-month service is due and you have only travelled 10k you have to do the 40k or 24 month service (the vehicle is two years old). In additional many logbook service have notations about severe operating conditions. Conditions like extended towing, off road use or commercial use. It is tricker than it sounds.

General Service:
General services are routine maintenance tasks that may not necessarily adhere strictly to the manufacturer's logbook recommendations. They are often performed at regular intervals every 6 or 12 months.
Tasks may include:
Oil and oil filter changes.
Visual inspection of the vehicle components.
Fluid level checks and top-ups.
Inspection of lights, wipers, and other basic components.
Tire pressure check and adjustment.
Safety checks.
General services are more flexible and may be tailored to the specific needs of the vehicle or the preferences of the owner. They cover essential maintenance tasks and safety checks like brakes. When we perform a general service the list of maintenance and safety checks performed is long and detailed especially for a vehicle we have not seen previously and we have no history off.
In a nutshell a general service is suited to a vehicles outside of the manufacturer’s warranty and vehicles outside the scope of the logbook due to age or limited milage travelled. Of course the logbook service could be performed on these vehicles however it is recommended to do additional checks over and above the logbook due to age or the limited distance travelled.