@Parodius it is very sensible of your trainer to refer you to a canine behaviourist, however you don't need a vet referral.
In essence a trainer "trains" the handler, giving guidance on skills such as recall, relaxed lead walking etc..
A behaviourist works with the handler on issues where the dog's emotional state is leading to some issues.
Saying that there are some amazing trainers who have a very good handle on the behaviour side of things, and behaviourist who struggle with the "training" side of things. Most are happy to chat on the phone, so you can get a "feel" for who would suit you and your dog.
Vets are important, as a high percentage of behaviour cases have some underlying discomfort or pain.
I work with the clients vet right at the outset, letting them know that one of their patients is a client of mine. I share the initial detailed questionnaire and work with them to rule out any medical reasons for the behaviour the dog is presenting with. Sometimes medication is required, and although a behaviourist role is not to advise on medication, they do need to have a good working knowledge of what is available to help support clients, through monitoring progress etc..
So that is the difference between a trainer and behaviourist.
It does get a bit complicated.
You have different tiers of qualifications. Generally speaking you need to see evidence of additional academic accreditations along with some experience to qualify as a behaviourist.
So look for:
IMDTB
CCAB
ABTC
There are probably a couple more associations, but those are the ones of the top of my head.
Also make sure they are keeping up with CPD - "continuing professional development"
Hope that helps!