Can two players with the same rating have very different skills?

I "GET" that the rating system is a very good representation of our real potential as a chess player but there are different ways two players can get to the same rating.

This is of course more applicable to the faster formats of chess..There certain players who get there by playing the tougher guys, while the others would like to "preserve" their rating or "milk" the advantages of repeatedly playing weaker guy.

Dont get me wrong, I have nothing against one or the other type.But the question I am trying to address is: 

Can two players who have used different routes to get to the same rating , have completely different potential as chess players?

I believe its possible. An views?

Considering that two players who have used the same route to get the same rating can have different skills and potentials (skill doesn't equal potential), then yes, I think if they used two different routes this will also be true.

But if the ratings are stable over many games vs a variety of opponents, then I don't believe their skills are very different.  Easily within 100 points I would guess.

Of course in a head to head match one may have an advantage due to style or particular strengths vs their opponent.  e.g. a trappy opening in blitz games the other has never seen.

As for weaker vs stronger, it's just a mathematical formula.  You have the same chance of beating a lower rated player many times as you do a stronger player once... and the statistics take this into account when awarding points after the game.

In fact the difference in ratings is the only variable the (basic) formula takes into account.

Thanks , Waffle :).

Let me put this in perspective. If there is Mrx -who chooses to play only ratings 1600-1800 as opponents, and stubbornly so . He lands up winning some  and losing some.Then There is Mr Y - who keeps playing 1300 - 1400 s. They have been doing this for ages now , and havent deviated from this practice.Their ratings are 1611 (say). Who will win on a best of 11 games between x and Y? Does your answer remain"50/50" - I wouldnt agree!

Then

Yeah or just in the case when one player is constantly improving, your rating will never catch up with your ability, so if you meet players with stable ratings you will be better.

It's been over 20 online games since I've lost to anyone less than 100 points better.

ditto fedtel

It's difficult to say their ratings are not comparable based on the ratings of their opponents.

i.e. you're assuming the opponent's ratings are reached using a even distribution and skill set while Mr X and Mr Y are the only ones who have skewed ratings.

What happens when the 1400s Mr. Y faces play 1700s all the time?  But what if those 1700s play 1400s all the time?  Or if the 1700s are tired and he gets a few easy wins before the 1700s log off?

I may also try to argue it's statistically harder to maintain a rating vs lower rated opponents because it's more likely to beat a player rated 300 points higher once (say you get lucky) than it is to beat a lower rated player 10 times in a row (consistency is difficult to maintain).

But the truth is if you play many games vs many different opponents, your rating is a very good estimate.  I think the two players you suggest would be fairly close in skill.

i dont see this happening, the guy constantly playing higher ratings is unlikely to stay at the same rating as a guy who plays lower. This is becaue playing higher rated players makes you improve quicker.

But for the purpose of the hypothetical situation, I believe they would be equal. 

Yeah, Fedtel, I agree with you. I want to add that, in my oppinion, the one who plays against better opponents than him (and usually loses), would be better than the other who plays against lower rated player (and usually wins) because the first must be trained to play under more difficult circumstances (assuming they now have the same ratings). So Rajbhalla, I think the chances are at least 70-30 for Mr Y 

The rating formulas presume that the players are playing against the same pool of players. 

If two players consistently hand-pick their opponents, then they aren't participating in the same pool of players.

Ergo, the two ratings really aren't comparable. The 1600 who plays up all the time might really be an 1800 player in the common pool, but has had his rating deflated by playing up consistently. Or he  might really be a 1300 who has kept his rating artificially inflated by not losing so many points by playing up all the time. Likewise the guy who plays down might really be a strong 1200, or whatever. 

Most rating scandles in chess have revolved around people selecting their opponents. The results have tended to be to artificially inflate ratings. But it is also possible to work the other way. 

In my level, i do not know any about 1.e4 with white. But maybe others do...