For instance, if one LED is rated 1000 Lumens with a ten degree pattern, and the next one is rated the same 1000 Lumens but a 20 degree pattern...the second bulb is covering four times as much area with that same brightness.
No lumens is the total amount of light put out by a luminare integrated over a sphere or (360 degrees if you like).
2 LEDs putting out 800 lumens will emit the same amount of light.
One fitting can produce a brighter spot than another by concentrating the light with say a reflector, but the sidespill will decrease and the total output will be unchanged.
Relying on specifications is not a good way to judge LED products from different manufacturers as the values quoted are often calculated (or made up ) in different ways.
If you can find the type of led or leds used this is often the best way to compare products, but many manufacturers only list the most basic information.