Level 1 and 2 EVSEs are ACV charging. In the USA, a level 1 device is using 120vac, and a level 2 device is 240vac. It gets a little more complicated in other markets. The level 1 device BMW provides with US cars is a 120vac device...depending on the MY, it may be 10 or 12A.
DCV charging bypasses the car's AC-DC converters, and feeds, nearly directly, into the batteries themselves.
In reality, level 1 and 2 devices are not "chargers", they're fancy on/off power switches...the charger is built into the vehicle.
A DC device IS a charger, as it provides DCV.
Most cars other than Tesla are somewhat limited in the maximum current DCV input they will accept. On the i3, today, that maximum is 50Kw. When charging with ACV, it's about 7.4Kw, depending on the market, it might be a bit more. The Tesla is over 100Kw.
The newest CCS (DC chargers) being installed can handle up to 350Kw, nearly 3x the max of a Tesla. They also support higher voltage battery systems (800V verses the 400V max of the majority of cars out there).
Just like you may find an EVSE that has limited maximum output, the same is true of CCS units. There's a signalling system between the car and the device that negotiates the max available, and what the vehicle needs so that they can cooperatively get it all right without damaging either the vehicle or what it's attached to.
No cars today can handle the maximum throughout the whole charging session...they all require things to taper off as the charge level gets near maximum. So, the last 10% or so (varies) can take nearly as long as the first 90%. The holy grail is a battery system that can handle a very rapid charge to full without delays. We're getting closer, but that's still years away. Some of that is because of heat buildup, and the method and quality of the cooling system for the battery can go a long ways towards maximizing it's overall health and longevity as is the method used to throttle the charging rate to preserve the batteries. Liquid cooling like the i3 has works much better than the air cooling used on the Nissan Leaf, letting the BMW battery to have a more reliable, longer-lasting battery life.