My understanding is that "sarcastic" remarks are blatant and obvious lies whose intentions are opposite their literal meaning. For example it would likely be sarcastic of me to say "what a perfect day for a picnic" during a snow storm. "Snide" is a bit more difficult to explain, as it's meaning is a bit abstract. Overall, I believe to be snide is to insult someone indirectly or mockingly. Snide comments are often sarcastic also. For example, if someone were to reply to this post of mine writing "wow, what a great explanation of snide and sarcastic! You must be the greatest genius of the century!" I would assume they were being quite snide and sarcastic.

Snide is more mocking and can be nasty, sarcasm is mocking too but more for irony

These words are not synonyms. Calling someone “snide” is an insult or negative remark towards them- whereas calling someone “sarcastic” can sometimes be a compliment.