Two questions that decide which system you are dealing with
Question one: does the problem only happen when it rains? Question two: is any waste water involved — anything from a toilet, sink, shower or laundry?
A problem that appears only during or just after rain, with no waste water anywhere, is a stormwater problem. Stormwater is a separate pipe system carrying rain from roofs, gutters and paved surfaces. It has its own inlets, its own pits and its own blockages, and nothing done to the sewer drain affects it in any way.
A problem involving waste water — regardless of the weather — is the sanitary drain. That system runs whenever anyone in the building uses water, so its symptoms do not care whether it is raining.
The confusing case is a property where both are happening, which is more common than it sounds because the two systems often share the same ground and the same causes: roots, settlement and damaged pipe do not distinguish between them. If you have waste water backing up indoors and a pit surcharging outside during rain, you may genuinely have two problems, and saying so on the call is far more useful than describing it as one.
The reason this is worth getting right before anyone attends is simply that they are different pipes with different access points. A visit spent on the wrong system is a visit spent, and the original problem is still there when the next rain arrives.