Update: Better terminology is “micro payment” for the tiny monetary transactions, and “virtual goods” for the things you buy through an in-game store. I had previously equated “micro transaction” with “micro payment” exclusively.
A typical implementation of micro transactions in a game environment would be LOTRO's Turbine Points, where real money is exchanged for (non-refundable) store credit in the form of Turbine Points, which are then used to buy items from the Turbine Store. Another example is Global Agenda where real money is exchanged for (non-refundable) store credit in the form of Agenda Points, which are then used to buy items form the virtual goods stores.
In EVE Online, we have had micro transactions for a long time in the form of PLEX. Some people will argue that PLEX is a form of RMT, which is true! PLEX is RMT in addition to being a form of store credit. Note that in EVE we have two stores: the general Market with ISK currency, and the Noble Exchange with Aurum currency. These two currencies do not easily translate to Turbine Points or Agenda Points, since there is an intermediate currency which is converted to either of these two by some mechanism (trading PLEX for ISK or surrendering PLEX for Aurum, respectively).
RMT and MT are not exclusive concepts. In fact MT is a complete subset of RMT. In one case, someone is spending real money for something normally acquired in-game, in the other someone is spending small amounts of real money equivalent to acquire goods in-game. From the buyer's point of view, real money changes hands, “store credit” appears in the game. Store credit in EVE might be ISK or Aurum: it doesn't matter whether the ISK is created by CCP or farmed by a player. For the purpose of RMT, real money has changed hands one way, in order for virtual stuff to change hands the other way.
The only distinction between RMT and MT is that micro transactions by definition involve small amounts, and some system has been put in place to reduce the cost of individual transactions. The purpose of a MT store with its own currency (e.g.: Turbine Points) is to provide the means to amortise the cost of the real money transaction over a large number of smaller transactions. There is no requirement for MT currency to be separate from in-game currency: this is an artificial restriction put in place by Free-to-Play games in order to prevent players funding their store purchases by simply grinding for currency.
Of course in EVE Online there is a distinction between legitimate and illegitimate RMT. In one case, the buyer is sending their real money to CCP, in the other they're sending real money to someone else who is not CCP. The fact that this distinction exists doesn't prevent MT being a complete subset of RMT.
The aim of a micro transaction system in an online game, for example, is to allow players to buy some in-game advantage for a few tens of cents. They might be playing Farmville and be able to buy better seeds for a dollar (using Facebook credits or Zynga coins). They might be playing Cow Clicker, with the micro transaction being the purchase of a different colour or style of cow for a few dollars. They might be playing EVE Online, with a micro transaction being the purchase of a Rifter, a few thousand rounds of RF EMP S, and some auto cannons. I would not class the purchase of a Titan or Supercarrier as a micro-transaction, even though it uses the same system: this is purely because the purchase price of a Supercarrier is far in excess of the equivalent of an hour's worth of average salary in most countries (there might be some people who make hundreds of dollars an hour, but I don't know any).
Without the ability to trade GTC or PLEX for ISK, there would be no legitimate RMT in EVE Online. The presence of PLEX doesn't suddenly make RMT possible, it just makes RMT legitimate. The fact that a RMT system is not specifically designed to cater to micro transactions doesn't prevent micro transactions happening: the presence of gold sellers catering to World of Warcraft players provides for micro transactions through illegitimate RMT.
To recap, a micro transaction is a purchase that constitutes a small amount of money (my arbitrary limit is that it must be less than one hour of the average salary in the purchaser's country of residence), with some supporting system in place to reduce the per-transaction cost of each of these smaller purchases. The supporting system doesn't have to be an official part of the game, assuming that illegitimate RMT is possible. If Trustworthy Terry down at the pub can trade me 1B ISK for $US30, that sets the approximate limit for a micro transaction in EVE Online to about 300M ISK. The fact that the deal was illegitimate in CCP's eyes is irrelevant (well, right up to the point where my in-game currency is confiscated and my wallet ends up negative).