Hi Frog, yes, I agree, SEN and SN do have a very broad designation, that's why I said many, not all.
e.g. Autism is a lifelong, developmental disability that affects how a person communicates with and relates to other people, and how they experience the world around them.
The characteristics of autism vary from one person to another, but in order for a diagnosis to be made, a person will usually be assessed as having had persistent difficulties with social communication and social interaction and restricted and repetitive patterns of behaviours, activities or interests since early childhood, to the extent that these "limit and impair everyday functioning".
from here www.autism.org.uk/about/what-is/asd.aspx
For example, not all kids dxd with ADHD will be automatically classed as socially vulnerable, but some will need support as their impulsivity overcomes their self-preservation instincts, running into traffic, climbing and leaping without ascertaining a safe landing etc.
I know those actions can also be caused by sensory processing issues and likely other co-morbids, but I think I'd rather be the parent that was offered suitable therapy for my child, rather than the parent whose child was denied suitable therapy as their diagnosis alone excluded them.
The OP said they are thinking of funding therapies to help "vulnerable children" so don't want to exclude any child who may benefit when they define their criteria to obtain that help. " We can be loose in our definition but specific in our work (which is what we intend) but we don't want to shoehorn ourselves in such a way we cant diversify in future or have to go through this whole exercise again."
On that basis, I'd say include SEN and SN in the definitive criteria, simply because it would be a real shame if any child with SEN and/or SN who could benefit was excluded because their individual diagnosis did not immediately suggest vulnerability but their presentation or co-morbids did.