Many aircraft systems operate using a multiple-logic system. ie: if criteria a, b, and c are met then x,y,z will happen. Depending on what aircraft type, "weight-on-wheels," "truck tilt" or "ground sensing" plays a role in many systems such as anti-skid, ground spoilers, autobrakes, pressurization, and even engine idle speed to name a few. And sometimes manufacturers will update or change the logic of a particular type aircraft in later production runs. So an early 737-300 for example might have a slightly different logic for spoiler operation than a 737-300 built years later.
On the 757/767, if we have an AUTO SPD BRK light we can not arm the speed brakes for landing at all, even with the gear down, and they have to be operated manually after touchdown. This doesn't mean that they wouldn't work properly if armed. It only means that there is a fault in the logic which could affect the redundancy built into the system for safety reasons. Therefore you could be just one more small fault away from having full ground spoilers deployed in flight. (Not a good thing during an approach when low to the ground.)
As for different airlines having different procedures, often the person who wrote the manual for the airline (could have been decades ago in some cases) may have felt it was prudent to have an additional level of redudancy. When the manual is approved by the FAA they make sure that all of the manufacturers required procedures are covered, and if the airline chooses to add additional safety measures, they will usually sign off on it, as long as it is more conservative. Once it has the blessing of the FAA it is written in stone for that airline, and changing it is usually a long and costly process. This is why airlines who fly the same type aircraft have different operating procedures, and you can't just take a pilot from one airline and stick them in another airline's aircraft.
Not to get off on a tangent here, but it is an interesting example of how these differences arise. When TWA first took delivery of the L1011, someone there decided that an overhead switch should be flipped forward for "ON" and backward for "OFF." (I may have that reversed, it's been may years since I was a 1011 engineer.) Anyway, Lockheed designed them the other way, so all of TWA's 1011's were modified to reverse the switch position. The problem becomes obvious when you consider the pilot of another airline coming over and trying to fly a TWA 1011, and flipping all the switches the wrong way! Either the pilots need to be retrained, or the airplanes converted.
Hope this answers your question.