What really is the difference between the "ideal variety" (Lancaster) of a differentiated product approach and the "love of variety" (Dixit and Stiglitz) approach?
Basically, the difference is that in the love of variety approach the entry of new varieties in the market does not "crowd" variety space. So, differentiated varieties may exhibit a high or low degree of substitutability, but this is invariant to the number of products in the market. Hence, consumers "love" variety, in the sense that increased variety improves welfare.
In the Lancaster ideal variety approach, entry of new varieties causes "crowding". Goods become more substitutable as more varieties enter the market. So, the marginal utility of new varieties falls as the market size grows.
These two approaches have different implications for welfare of small and large countries as discussed in Hummels and Lugovskyy.
The "ideal variety" approach proposed by Lancaster focuses on the consumer's preference for a particular set of product characteristics, rather than the number of varieties available in the market. In this approach, consumers have a specific set of ideal characteristics in mind when they make purchasing decisions, and they will choose the product that comes closest to meeting those ideal characteristics.
On the other hand, the "love of variety" approach proposed by Dixit and Stiglitz emphasizes the role of variety in consumer welfare. In this approach, consumers derive utility not only from the particular characteristics of a product, but also from having a choice of products with different characteristics. The more variety available in the market, the greater the potential for consumer welfare improvement.
So, while the "ideal variety" approach focuses on the specific product characteristics that consumers desire, the "love of variety" approach emphasizes the role of variety itself in consumer welfare.