Pedagogic grammar (/pedəgɒʤɪk græmə/) or pedagogical grammar (/pedəgɒʤɪkəl græmə/) is grammar as it is presented to students, particularly those learning a foreign language, as opposed to scientific grammar which is used by linguists.
Pedagogic grammar is often rather simplistic with the hope that this that it can be more readily understood by students (and teachers). It tends to ignore exceptions to rules, in favour of presenting more general concepts. Pedagogic grammar also tends to focus on difficulties students have with language rather than scientific grammar which tends to focus on the language as a whole.
As for grammar on the internet, since anyone can write a grammar website, it does mean that grammar information found online can range from useful and accurate, to extremely unreliable and wrong. Such information may also be incorrect if it reflects traditional grammar rather than modern grammar. Incorrect information can contribute to the creation or perpetuation of language myths.
A pedagogic grammar book is a book for students.