No, it's still a general officer rank. The officer commands a brigade, hence the term "brigadier". Perhaps the confusion is that this might be a colonel's command in the US Army, as a Commonwealth brigade = a US regiment.
Canadian brigades have been commanded by Colonels for about 12 years now. Aussie brigades too. Not sure about our British friends.
A regiment is no longer
normally deployed as a fighting formation in its own right, they way it might have been in the Civil War. It is more typically an administrative affiliation of similar units. Battalion-sized armoured (armored) and other cavalry units are referred to as Regiments, but in Commonwealth nomenclature the infantry corps is divided into regiments normally comprising 3 battalions (ie. 1st Battalion PPCLI, 2nd Battalion PPCLI, etc) But those battalions don't fight as a Regiment - when they come together to fight they fight as part of a brigade, which in larger armies will deploy as part of a division.
The norm is for brigades to actually fight as brigade groups (the US calls them brigade combat teams), the difference being that a brigade group has integral armour, artillery, engineer, and combat service support units while a brigade comprises a unique arm (ie. an infantry brigade, armoured brigade, artillery, CSS) which requires divisional support in order to obtain the services of its sister arms.
Typically, however, most nations other than the US and Russia deploy only beefed-up battalions on their missions, usually called battle groups since they have additional assets attached to them (tanks, CSS, etc at company strength). The UK deployed a brigade to Iraq and it almost crippled the British Army to maintain so large a force overseas.
The Soviet system employed regiments as a fighting formation, though. I think the Chinese as well. Confusing enough? lol.