Learn English – What’s the difference between Media and Press

1. Suasive is an adjective that, in Linguistics (Grammar), "denotes a class of English verbs, for example, insist, whose meaning includes the notion of persuading and that take a subordinate clause whose verb may either be in the subjunctive or take a modal."

2. Persuasive is an adjective as well, that means being "good at persuading someone to do or believe something through reasoning or the use of temptation: an informative and persuasive speech." OR "She was very persuasive!"

The difference, then, is that while the former denotes a grammatical class for verbs, the second is adopted the way you already know, with people, situations, etc.

EDIT NOTE: In the OED it says that a speech can be "suasive" but considering the OALD and my dictionary didn't have it, I supposed it was an old use or it fell into disuse. So I checked the Ngram on google and it confirmed what Billare said and what I was thinking.

As defined from the NOAD, grammar is, "the whole system and structure of a language or of languages in general, usually taken as consisting of syntax and morphology (including inflections) and sometimes also phonology and semantics."

It includes the syntax, but it's not limited to that.

The syntax of a language is, "the arrangement of words and phrases to create well-formed sentences in a language."
For example, the syntax is about which order subject, verb, and object have in a sentence to form a well-formed sentence. A sentence like "like it I" is not considered a well-formed sentence, basing on the English syntax, even if people would understand that the correct sentence is "I like it."