"Traditional grammar" refers to the description of particular languages (their phonology, parts of speech, word order, inflectional paradigms, etc.). This is the basis of modern linguistics, but modern linguistics goes further and also tries to explain lots of other things, such as how we acquire language, how languages evolve and are related to each other, the cognitive processes behind human language, etc.

I might say basic grammar. 

There are basics but then some areas are slighly different (can be seen as dialects).

In Honduras they speak Spanish so others can understand but as a family they will speak in a way just they know or town compared to another town might use special words for something that no one else understands.

Another example set is in USA is that English is basic language rules, but Texas or Southern states say things differently Miss or Mrs. could be ma'am in southern states. No is NAW in Texas if you didn't know NAW (nah) was no you might be a little confused when someone used it but the sentence structure would be the same.