Is it normal? Well, quite honestly, I reckon very little is normal in the world of neuros and MS!
I bet the fact you saw someone else the first time has caused this situation though in that perhaps the new guy’s assuming that your current symptoms are an extension of the original relapse rather than a new one or that they are not sufficiently separate to be able to know for sure? That’s the only way it makes any sense at all to me anyway.
The official definition of a relapse includes a line that says that the new symptoms have to start more than a month since the last relapse started - this is because relapses sometimes sort of cascade - they start with one thing, then a couple of weeks later another thing happens, then another, etc, etc. These kind of relapses can last a long time so your current symptoms could maybe be part of the first relapse, or at least appear that way to him.
The good news is that you are seeing an MS specialist now. He may be a bit on the indecisive side(!), but he should be able to get you all the help you need if and when you need it.
If you want to push for a diagnosis now, rather than wait for a relapse, then I suggest you enrol your GP. If your GP has seen two separate episodes with different symptoms and writes to tell the neuro that, then it’s possible that he might reconsider. The potential downside is that you challenge the guy who you are going to rely on from now on - which is not necessarily ideal. Perhaps your GP would be willing to take the fall for you? As in making it clear that it is her that is challenging the diagnosis, not you.
Remember that the only potential upside to getting the diagnosis now is to get access to DMDs - you are already getting everything else - and he may say no to that at the moment because your relapses may not be “two clinically significant attacks” in his eyes (hence the dragging of his feet on the diagnosis). So, it might be better to wait? (Although you could always ask your GP to ask for DMDs in her letter, if it gets sent - that might clarify things?)
The reason the neuro said that it was “only words” is that in his mind MS is a chronic condition so there’s no rush. He knows you’ve got MS, but he wants to tick all the boxes properly before confirming it. We are always in a bigger rush than the neuros - if it was them who actually had the symptoms, they would be too!