There are three different known D-Dial models, and one belongs to each of the three Deviluke princesses. They all resemble cell phones and aid the weilder similarly, but there are still a few unique aspects to each model.
Nana's D-Dial summons all kinds of animals and creatures. This particular model is the only one we've seen where the weilder has been able to use it to create a portal to the realm it summons from.
Momo's D-Dial summons all kinds of plants and flowers. Appearing and summoning nearly exactly like Nana's model, Momo can presumably create a portal to the realm her particular model summons from like her twin can, but we have not actually seen Momo do that.
Lala's D-Dial is the most unique. It's appearance differs slightly to resemble her signature Dressform outfit, and it summons her many inventions instead of any living thing. Nana and Momo's models "transfer," while Lala's model "transmits," suggesting it either utilizes the Transfer System in its own way to summon her inventions in the same realm as the signal it sends or it's simply its own teleportation system.