The phrase, "Affiliates are an extended sales force for your business", which is often used to explain affiliate marketing, is not completely accurate. The primary difference between the two is that affiliate marketers provide little if any influence on a possible prospect in the conversion process once that prospect is directed to the advertiser's website. The sales team of the advertiser, however, does have the control and influence up to the point where the prospect either a) signs the contract, or b) completes the purchase.
Analytics are limited. Unlike with conversions made directly on your WordPress site, you’ll be limited in terms of what you can learn about the people making purchases through your affiliate links. While Amazon does provide you with details about clicks and sales, you won’t get deep insights into who the consumer was and what they did on your site before they got to that point that you would with Google Analytics.