IELTS teachers often categorises IELTS essays differently and also give them different names.
1. For the opinion essay (Do you agree or disagree? / To what extent do you agree?), some teachers call this the argumentative essay, persuasive essay or agree disagree essay.
2. The discussion essay generally has the same name but some teachers include the advantage/disadvantage essay in this category while I like to distinguish it and teach it separately.
3. The solution essay is also often categorised similarly by teachers but don’t forget that this also includes a cause/solution essay as well.
4. The direct questions essay is sometimes called the two question essay but as it is possible to get three questions I prefer the name direct questions essay.
5. I haven’t come across any teachers categorising an IELTS essay as a narrative essay but no doubt there are some who do.
I know it can be confusing to have teachers categorising essays differently and giving them different names. I recommend you look through the IELTS Cambridge books 1-9 and see all the types of essays that come in IELTS writing task 2 for yourself.
Here is the list of persuasive essay topics , which you can use for your reference.