Sold by Amazon.com
These two indicate who holds the stock and who delivers the product. All prime-eligible items are shipped by Amazon.com (although some other shipping methods provide 'prime free shipping', without a 2-day guarantee), while Amazon also will wholesale buy and sell items themselves if they're high-volume enough, which is indicated by 'Sold by Amazon.com'.
The whole 'Visit the <Brand> Store' is a way to go to a page that only shows products sold under that brand/company. For example, this Corsair ql120[0] has "Visit the Corsair store" under the product name which shows all Corsair products. Amazon generally limits the amount of off-Amazon linking done, although it's not strict and it's not off-limits in product images or the description.
