4.4V vs 3.7V LiPo -- Is there such a thing?
4.4 V and 3.7 V here refer to different characteristics.  


3.7 V is the nominal voltage (average voltage during a complete discharge) of a "traditional" LiCoO 2 -based lithium ion cell. Such a cell typically has a minimum voltage around 3.0 V, a maximum voltage around 4.2 V and a nominal voltage between 3.6 and 3.7 V.  
4.4 V refers to the maximum voltage of cells with an improved anode that can endure higher voltages. These cells tend to have a similar minimum voltage, but the maximum voltage is between 4.35 V and 4.4 V. Since they can be charged further, the nominal voltage is also increased to around 3.8 V. This improvement is achieved with silicon and graphene -containing additives  


In the radio control world these are explicitly marketed as "LiHV" etc, but they are increasingly common in all sorts of products like mobile phones.

There are several research papers on the subject, e.g. http://m.jes.ecsdl.org/content/164/1/A6075.abstract