I believe the main difference between bouillabaisse and bourride is that bourride is thickened with aioli whereas bouillabaisse, uniquely, is basically oil and water boiled rapidly together to achieve an emulsion. The bourrides I have tried have never contained tomatoes either. In the end, I found restaurant bouillabaisse to be a complete disappointment, unlike bourride or matelote or cotriade, all of which I have greatly enjoyed on trips to France. All these places in Toulon or Marseilles or wherever, with access to the right ingredients, seemed to screw up the dish by being omitting or being stingy with the conger eel (my favourite part), serving badly cooked potatoes, not achieving a good emulsion, adding too much or too little saffron, being overcautious with the pepper, or whatever. Factor in the various constraints of restaurant service, and my feeling is that if your kitchen happened to be in the right location, you would do much better to return this preparation to its homely origins, make it lovingly and serve it casually, rather some in artful presentation which is briefly shown to the client and then whisked away to the other side of the restaurant, or even outside onto the street, as at Miramar.