Warfare measures your ability to fight with weapons, and your strategic, tactical, and organizational skills. You use it for everything from playing chess to managing a business to leading armies to sword fighting. It does not, however, cover unarmed combat, which is the realm of Strength.
Warfare also covers a lot of other skills which revolve around tool use, from hacking to wood-carving to driving.
Drake, Juri, Moonshade, and Utena rule here.
Warfare applies to more than just the sphere of combat. It tends to apply to any sort of conflict or activity which involves the use of tools that aren't controlled directly by will. It also encompasses organizational skills. Thus, high weapon skills also makes you a good sculptor, and high tactics lets you run a business.
The two halves of warfare are often interwoven in various activities. For example, a chase scene. Weapon Skills determines how good at the technical aspects of driving you are, such as how nimbly your vehicle will turn, or how well you can make it dodge incoming missile fire. Tactics, on the other hand, tells you the best route to follow to throw off the people chasing you or the best stunt to try to pull off with your WS in order to make them wreck.
Tactics also can be used in conjunction with martial arts in order to coordinate groups of martial artists or to most effectively fight a large group of people with martial arts. (Or, for example, to help you lead a football team to victory.)
This applies effectively to both Martial Arts and Weapon Skills forms of combat.
What happens when Gerard (Strength 140, Martial Arts 130, Physical Strength 150) decides to throw down with the Master and students of the Borli Dojo all at once? (The Master has Str 35, MA 40, PS 30, he has three students who are Str 20, MA 25, PS 15, a dozen students who are Strength 5, MA 7, PS 3, and twenty novices who are all Amber Strength.)
In theory, that's 130 points of Martial Arts against 170 points of Ranked Martial Arts, plus twenty people who have Amber Strength. One might expect Gerard to lose. Except...
First of all, Gerard can clobber 32 out of his 36 foes with a single punch each. His Physical Strength is so high that he can pretty much ignore most of their blows long enough to do this. This reduces the opposition to 120 points which he has an advantage over.
Secondly, Gerard's foes can't just add their strength together directly to face him under all circumstances. If Gerard has superior tactics, then Gerard can pretty much force them all to pit their skills against his individually, manuevering them into getting into each other's ways and striking each other while he mocks them with his monkey pants. Their superior numbers will still play some role in the battle, but not enough to make a real difference, given the disparity in skills involved. In which case, none of them has a prayer of hitting him, and given the time to punch them all out, he will.
If Gerard has less tactics than all of his foes, he is in trouble, as they will be able to meld their skills together perfectly against him, and he will likely go down under the tide of foes. (Effectively adding their MA together into a collective MA total). He will likely take a fair number of them with him because when he hits one of them, they can't pool their damage resistance, but he's likely in big trouble.
The more likely case is that a few of his foes may have superior tactics, while the majority of his foes do not. In that case, his foe can try to coordinate the rest of his foes against him, but it will not be as effective as if they all beat him in tactics. How effective the coordination will be depends on how much the foe beats Gerard and how good the tactics of those being coordinated is.
While this example uses Martial Arts, the same principle applies to Weapon Skill use.
Coordinated assault can fail miserably even if the coordinated attacks all have a tactical advantage on their foe if the sum of their skills is insufficient. If an army of Hyper-Augmented Napoleons (Tactics 80, Martial Arts Chaos, Strength Chaos) all attack Gerard in unison, he will likely still win unless they come in extremely huge numbers because even with perfect coordination of their skills, he will still be better than them as a collectivity.
Coordinated assault can also sometimes be limited by environmental circumstances. Only so many people can try to melee with a foe at a time. This is how Bleys was able to fight his way up the steps of Kolvir, even with Benedict coordinating the defense against him.
It is harder to dodge a blow than to parry it in close combat. Blows with more strength behind them become harder to parry, however, so you may choose to dodge incoming blows instead of parrying them. This gives your foe an advantage which varies by how much reach his weapon has (dodging someone who has a knife is easier than trying to dodge someone with a quarterstaff). This disadvantage is one of the aspects of why MA has a disadvantage against Weapon Skills. (A MA who has armored gauntlets, etc, thus loses some of his disadvantage as he can now parry blows.)