Since then barriers have also been fitted to many AOCLs.
AOCL: Automatic Open Crossing Locally monitored
AOCR: Automatic Open Crossing Remotely monitored
An AOCL that has had half-barriers fitted is an ABCL Automatic Barrier Crossing Locally Monitored.
The other type of automatic crossing is the AHB Automatic Half Barriers. If they were being introduced now they would probably be designated as ABCR for consistency, but they got their name when they were the first and only type of automatic crossing in the UK.
An AOCR is basically an AHB without barriers. Both were intended for use on relatively high speed lines. At the point at which the train activates the crossing, it is too late to stop the train if the crossing fails to work. There is therefore no point in providing driver's white lights, and so any failure is indicated to the signaller. This can require an expensive communication link to what are often very rural and isolated crossings. Both these types of crossing seem to have fallen out of favour, with many AHBs also converted to manned barriers.
AOCLs and ABCLs are used on relatively low speed lines. The train will be going slowly enough that it can stop if the driver sees that the crossing is obstructed or the driver's white light isn't flashing. As the crossing status is indicated to the train drivers, there is generally no status indication transmitted to the signaller. Note that the flashing white light at an ABCL generally doesn't prove the barriers down, as doing so would mean the light would start flashing too late causing the driver to start braking.
As the operating and failure modes of the two categories of crossing (locally or remotely monitored) are very different, they have very different control circuits.
Just to muddy the waters slightly, I understand that in Ireland (can't remember now north or south) they have some automatic crossings that are both locally and remotely monitored.