You cannot save the plane or the earth. It is essentially a big rock in space that is covered with dirt and water and is populated by a variety of species. The planet was here, it is here, and will be here short of a major disaster. The sun going nova or a giant meteor, the size of this planet, colliding with this planet might destroy this planet. Or maybe, on the off chance they exist, a hostile alien race decides that the universe is better off without this planet and blow earth up. Short of these scenarios, this planet will continue to exist, with or without humans. So, don't say save the planet or earth, you can't. Humans don't have the ability to destroy this planet, well, net yet.
As for saving the environment, all I have to say is that it is as much BS as saving the planet. Environment does not refer exclusively to the current state we live in on this planet. Mars has an environment, Jupiter has an environment, even the Sun has an environment. Granted, they are not very hospitable to us humans but they have environments. The term environment is too generic too mean anything.
I wish those people who came up with the above phrases have the decency to admit their selfish nature. Here, I said it, we are selfish and as such we should say "Save our current habitat" or "Preserve our current environment". Be specific, be honest, don't hide behind some generic, catchy phrases that have absolutely no meaning.