I'm not quite sure what your second sentence means. If you mean you want to merge the two threads into a single, more detailed diagram, I'd tend to avoid that. But this is only my opinion, it might not work for you.
As I said before, at a high level (little detail but a wide overview of the system) I would probably just show that a search could be invoked, and an answer received. Perhaps adding a UML note to inform the reader that more than one type of search could be used.
I would then provide a more detailed sequence diagram for each case, showing just what happens, and any differences that might be important - as before these could be expressed with additional elements, notes, or whatever (perhaps even UML Frames).
In order for the user, and your developers, to navigate these in a meaningful way, you might want to start with use cases at the same levels of detail. Here you could provide a high level use case for invoking a search, and show alternate scenarios for each type, once again identiying important differences. This allows you to introduce the elements and considerations you will elaborate in the sequence diagrams, and in other dynamic and structural diagrams elsewhere in the model.