Let's try to summarize your question before answering it:

• on the one hand concentration risk comes from the fact your book is highly correlated to few factors, hence you cannot take profit of diversification, market moves will affect you a lot;
• on the other hand wrong way risk is about being exposed to a counterparty such a way that the more you have products from it in your book, the more risk you have in them. General risk of this kind stems from underlying market wide relationships, and not from a badly designed product specific to one counterpart (it would be specific wrong way risk). Hence having this product from any counterpart will embed GWWR.

All this seems to mean that GWWR increases when you concentrate your book on products that are wrong way, and concentration risk is about... well... concentrate your book on few market factors. Then: what is the difference?

I guess the difference stems from where the exposure to the risk come from:

• for concentration risk, it is direct exposure to market factors it more or less increases the volatility of your book;
• for GWWR is about counterparty risk, to cite an ISDA doc:

[...] the credit quality of the counterparty may for non-specific reasons be held to be correlated with a macroeconomic factor which also affects the value of derivatives transactions.

Counterparty risk affects your book another way that increasing volatility: for instance it propagates a non linear way via CVA (Credit Valuation Adjustment) in your book.

My answer thus will be: if you do not value GWWR via counterparty channels (like CVA), but only by increasing the volatility of your book, you are right, there is not that much difference between concentration risk and GWWR in your procedures. But it is not the right way: these two risks should propagate in your book different ways.

Let's try to summarize your question before answering it:

• on the one hand concentration risk comes from the fact your book is highly correlated to few factors, hence you cannot take profit of diversification, market moves will affect you a lot;
• on the other hand wrong way risk is about being exposed to a counterparty such a way that the more you have products from it in your book, the more risk you have in them. General risk of this kind stems from underlying market wide relationships, and not from a badly designed product specific to one counterpart (it would be specific wrong way risk). Hence having this product from any counterpart will embed GWWR.

All this seems to mean that GWWR increases when you concentrate your book on products that are wrong way, and concentration risk is about... well... concentrate your book on few market factors. Then: what is the difference?

I guess the difference stems from where the exposure to the risk come from:

• for concentration risk, it is direct exposure to market factors it more or less increases the volatility of your book;
• for GWWR is about counterparty risk, to cite an ISDA doc:

[...] the credit quality of the counterparty may for non-specific reasons be held to be correlated with a macroeconomic factor which also affects the value of derivatives transactions.

Counterparty risk affects your book another way that increasing volatility: for instance it propagates a non linear way via CVA (Credit Valuation Adjustment) in your book. According to this US Interagency Supervisory Guidance on Counterparty Credit Risk Management document (p13 and beyond), counterparty risk management is not limited to CVA ; they list:

• counterparty limits, mainly via CVA;
• margin policies and practices, via haircuts, collateral and margining management;
• close-out policies and practices.

My answer thus will be: if you do not value GWWR via counterparty channels (like CVA), but only by increasing the volatility of your book, you are right, there is not that much difference between concentration risk and GWWR in your procedures. But it is not the right way: these two risks should propagate in your book different ways.