arietty once qualified you then tend to make a choice whether you want to go into either children on adult social work. The distinction is currently informal and in theory you can move between the two because social work is a generic qualification currently, but that might change in the near future.
Within each of those two general categories there are loads of different options.
In children's there is e.g. child protection, adoption and fostering, children with disabilities, youth offending. It's common in children's services for all the job vacancies to be in child protection and for people to move sideways into the other teams once they have 'sereved time' in child protection.
In adults services it much more depends on the way the council has decided to arrange its services, some councils offer 'generic' adult social care teams where the social workers will work with anyone over the age of 18 (learning disabilities, physical disabilities, older adults etc) others might have separate teams for each 'need'. It's common for hospital teams and mental health teams to be separate teams to other services as often some of the funding also comes from health. There has also been a recent drive for speciality Learning Disabilty and autism teams for similar reasons.
Within adults there may also be a couple of speciality posts such as alcohol and drug misuse social workers, or best interest assessors but these are quite specialist and would often be internal positions for more experienced workers.
There are lots of social workers employed in roles outside of local authorities such as in hospices or as independent mental capacity advocates, by cafcass etc. Their job title may not always be social worker though.
Many roles where social work would previously have been seen as an entry qualification now have their own entry routes e.g probation.
If it's domestic violence specifically that you want to work in you may be more interested in getting a qualification as an Independent Domestic Violence Advocate (IDVA).