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.