There is something to be said about the problems that have resulted from the very issue of pay-to-play. The problem is that its not just simply possible to classify it as a "pay to play" game, there are differences in quantification of their value add and their platform of playing - and its basis of its commercialization.
With MMOs, you have a very clear 1:1 value of purchase. The yielded "product" is the sustaining of the very service itself. No different than your internet service, cable TV, etc. These games have found that this isn't necessarily a sustainable model, as there is (as we all know) a clear disparity between those that can afford the monthly fee and those that cannot. Eventually if the game loses its overall worth, either by content, quality or service, then those that are minding the budget will leave with little convincing. That's the reason they went to the new micro-transaction model. By offering varied levels of shiny, the tab so to speak is picked up by those who can afford an excess... in effect carrying those who cannot, and allowing for all to play. In turn, the popularity of such an environment establishes word of mouth... as everyone wants to play with their friends. The ecosystem develops, and thus you have a reasonable model. This has worked for LOTR:O, STO and SWTOR. Even EVE online has adopted a model that is in the middle, whereby a user who is sufficiently established in the real world can purchase time for others, and establish their own fortunes in game thanks to the work of those who can't afford it in the medium but can afford it in the virtual.
In these cases the difference in overall representation is simple: You do not gain anything by the value adds except novelty. On the rare occasion you will get something of strength/power, but its not a permanent superiority: its merely early access. The entire reason it has become the model of success it is, is due to its availability to the masses in a harmless form: you get to pay for cosmetic differences only. This was actually the source of quite a bit of humor in season 1 of PA/PVP's The Trenches comic. There is nothing technically or physically better about the item, it only looks different or sounds different. But, it costs money... and it is unique. By being unique, one feels special - and by that it becomes valuable. That 14.99 item now becomes the monthly fee for someone else.
The other model, however, employs the opposite effect. This is the most visible one in the mobile world. Money buys you superiority. It may be in the form of bonuses (double exp, faster earning of money, whatever), or in the form of tangibles such as weapons or stronger characters. The most obvious one is the current games whereby you establish a limit on 'turns.' Those turns govern your advancement, access, worth... the person with money can move infinitely, the one without sits and waits. By the end of the week, they have no competition.
The goal in both is to make money. That is the business and that will always be business. The harm, is that its no longer a playing field where you're playing a game. Its buying the win. Since the business model works (they profit, who cares about the person?) the gaming industry shifts so that it continue to make that profit. Thus, you have DLC - the game is incomplete the first time you pay for it, so to play it you have to buy the rest. Though, you don't have to. But, an entire ecosystem is playing the cooler stuff... and you're sitting behind.
This business model is new. The reason its different from TCG, is TCG itself requires a tangible asset - you cannot play without the cards. Magic is nothing without a deck. To build a deck you must buy the cards. Invariably this means that to build a good deck, you must increase your chances to obtain a valuable card - thus you need to buy many boosters and decks. The model itself is simple, but its not exactly able to be changed - if cards are merely an imaginary item that one draws on their own, then the deck is never different. It reduces the unexpected and you remove the need for that extra bit of strategy. The ability to build a good deck is not necessarily tied to value, only the chance is increased the more you buy. The chance is always there - its never a zero value. In the pay to play games, the value is always tied to your success: there is no chance to your "strength" it is only your stats, items, level, money... whatever.
A good example of the difference is to compare it to a similar platform. There is a game in the app store(s) called Age of Warring Empires. It's your typical "build a city" "get 'cards' of various strengths representing characters' 'level them, build armies, attack others.' Well, every single one of those things has two ways of advancement: money or time. There is no way to get the best items without spending money. None. The only way to win, IS to buy the win. In magic, sure you have to buy the deck... but for all intents and purposes, there is a non-zero chance that first box you get builds a deck worth winning.