No, they're not equivalent. ARGs don't have (on the surface) anything to do specifically with RPGs over other genres. Note RPGs are a very broad category of games now, since they include a huge number of games that go by that term. Not all RPG videogames are actually "Role Playing".
The use of the term "RPG" (always meaning Role-playing games) has different meanings whether you are talking about videogame RPGs or non-videogame RPGs. If you are talking about non-videogame RPGs, then yes, ARGs and non-videogame RPGs do have alot of overlap, but aren't equivalent
So, if you're asking, is Final Fantasy an ARG? Nope. Is World of Warcraft an ARG? Nope.
Sure, you can take the basic words in the acronym ("alternate reality game"), and say, both of those are games that take place in an alternate reality, therefore they must be ARGs! But we give names to categorize specific types of games, and those names often are broader than the category they are trying to represent. Haps linked to I Love Bees - that is one of the more famous ARGs, and should be the starting point of your understanding of it. While I Love Bees was used to promote Halo 2, not every ARG has to be a marketing stunt.
Also, don't get Alternate Reality Games (ARGs) confused with Augmented Reality games (AR games).
Alternate Reality takes what already exists in reality (the internet, streets, phones, email), but plays the game inside of this reality. It's not using fake email systems and fake phones inside a virtual game, it's using the real email system the real phone system the real bus or subway system within the real world to play out a game. The game could be medieval fantasy, or sci-fi, or whatever. It doesn't have to use emails or phones - but the point is it takes place in this world, with less simulating, and more acting.
An RPG could be an ARG. An RPG doesn't have to be an ARG. Most computer/console videogame RPGs aren't ARGs.
Here's wikipedia's first-sentence descriptions: (Click through for more details on each one, if it's still unclear)
- Alternate Reality games: is an interactive networked narrative that uses the real world as a platform and uses transmedia storytelling to deliver a story that may be altered by participants' ideas or actions.
- Augmented Reality: is a live, direct or indirect, view of a physical, real-world environment whose elements are augmented (or supplemented) by computer-generated sensory input such as sound, video, graphics or GPS data.
- Virtual worlds: is a computer-simulated environment that can simulate physical presence in places in the real world or imagined worlds.
- Role-playing games: is a game in which players assume the roles of characters in a fictional setting.
- Role-playing games (in videogames): Single player role-playing video games form a loosely defined genre of computer and console games with origins in role-playing games such as Dungeons & Dragons, on which they base much of their terminology, settings, and game mechanics. This translation changes the experience of the game, providing a visual representation of the world but emphasizing statistical character development over collaborative, interactive storytelling.
- Role-playing: refers to the changing of one's behaviour to assume a role, either unconsciously to fill a social role, or consciously to act out an adopted role.
- Cos-play: short for "costume play", is an activity in which participants wear costumes and accessories to represent a specific character or idea from a work of fiction.
- Live-Action Role Playing (LARP): is a form of role-playing game where the participants physically act out their characters' actions.
See also Street Wars, and Urban-gaming.
Alternate Reality games (never heard them called ARGs before) are like Second-Life. They usually don't have an objective, but are like building an alternate version of your life. You buy a house, decorate it, open a buisness, etc... There is no real objective to the game, except interacting with other people. Alot of the time it is also more realistic. You live in a regular city (or a cruise ship as I recently saw in one game).
I don't think that's the commonly accepted use of the term 'ARG'. Second Life is not a ARG, in my opinion. It's a virtual world, like an MMOG, but not necessarily a game, so MMORPG doesn't apply - so we take a step back and call it a virtual environment or a virtual world (of which MMO is a subcategory).
Even Wikipedia's page of Second Life doesn't once use the term ARG to describe Second Life. It does use the term virtual world, though - 15 times.
I voted you down, but in retrospect, your post was a good one (helpful, polite, and informative), it was just that I think the information is inaccurate - at least, within the meager limitations of my own knowledge! 
Unfortunately I can't undo the downvote, so I upvoted one of your posts in another thread - feel free to correspondingly downvote mine if you think my post is inaccurate or unhelpful.
An ARG will tie-in to your real world experiences to put you into the state of the game. They often have elements that take place away from the computer, are widely social, and sometimes left with intentionally vague direction to encourage participants to collaborate together and share clues.
For example, Microsoft sent packages to participating players, hid clues in the content of seemingly unrelated websites, and arranged real-world phone calls and meetings to further the narrative of their ARG "
I Love Bees," which ran as an advertising campaign for another product. You can get a better idea of what a largescaleARG is like by seeing how that one played out.
This is more how I'm familiar with the term.
