Make no mistake, on initial operations against places like Basra (and the UK forces are still doing aggressive raids into town against Saddam's fighters), it was all arms, full equipment, body armour and helmets, the lot.
Where the differences are is right afterwards, it is felt that the best intelligence will come from the Iraqi people, so 'hearts and minds' swings into action, helmets off, berets on, sunglasses off, look these people in the eye, look less intimidating, interact, get the Arabic speaking personnel on patrol too.
They still have to be alert, but most of the troops would have done Ulster tours so they will be used to 'nonchalant-looking alertness'.
The current policy on Basra is called 'aid and raid', help the civil population, deal with the fighters, keep this up until Basra is pacified.
In truth, in general M.O. terms, the USMC
are closer to the British Army.
However, I don't think it is really about differences between armies, it more about recent experience and politics.
UK forces have conducted 'raid and aid' since WW2 in places like Cyprus, Aden, Borneo, Malaya as well as the 'aid to the civil power' in Northern Ireland and 'muscular peacekeeping' in places like the former Yugoslavia.
Jungle operations in Malaya and Borneo against insurgents were all about interacting with and winning the support of the locals, denying their villages to the enemy, gaining intelligence, then taking the fight to the insurgents, both of these campaigns were very successful, low key, with relatively small numbers of troops involved.
The US experience has been less happy, Vietnam, Lebanon, Somalia, the body politic has a policy of minimum risk to service people, plus it is felt that these sort of operations degrade effectiveness in 'war fighting', however the same forces that have conducted the UK operations above also did Korea, Suez, The Falklands and Gulf War 1, as well as having the bulk of the army geared to heavy armoured warfare in defence of Europe during the Cold War.
Also, the British Army tends to put NCO's in the firing line more with greater responsibility, a 21 year old corporal may well have led 4 or 8 man sections in the streets of Northern Ireland and the potentially more dangerous rural border areas on a couple of tours, also this is felt to help in the confused, frantic full urban warfare conditions, when communications from the command to the troops in action will be problematic.
Another factor is size, the UK forces in manpower to general population terms are small, they were by no means the biggest even during the Cold War, no conscription for over 40 years.
The US forces are part of a vast war machine.
The British Empire's influence on military culture still cannot be ruled out even now, for the most part, the forces defending and policing this far flung expanse of colonies was small.
However, I would not be surprised in 'raid and aid' is used on Baghdad if and when possible.
Apart from anything else, half the population of that city are under 15, never underestimate the P.R. front, this war is controversial enough as it is.