How to concat two different array types that extend/inherit the same type?

Just type assert the first array to a common type of the two array types:

checkOil((<Vehicle[]>buses).concat(trucks));

The casting to <Vehicle[]> should work

function checkOil(vehicles : Vehicle[]) {}

checkOil((<Vehicle[]>buses).concat(trucks));

Typescript will cast the (busses) to Vehicle[], and the same will be done with the rest

e.g. this will return (in console) two objects - Vehicles

class Vehicle
{
    public Type: string;
}
class Bus extends Vehicle
{
    public A: string;
}
class Truck extends Vehicle
{
    public B: number
}

var buses: Bus[] = [];
buses.push({Type: 'Bus', A : 'A1'});
var trucks: Truck[] = [];
trucks.push({ Type: 'Truck', B: 1 });

function checkOil(vehicles: Vehicle[]) : Vehicle[]
{
    return vehicles;
}
var result = checkOil((<Vehicle[]>buses).concat(trucks));
console.log(result)