Collision between registered trademark and app branding

While you can always use a mark in the U.S. without registering it, you do so with extraordinary risk under the circumstances that you describe. Assuming that the registered mark is highly similar or identical to your proposed mark and the goods/services of the registered mark are sufficiently related or in the same channels of trade as your goods/services, you use of the mark could expose you to liability for trademark infringement. That liability not only carries the risk of the registered mark owner being able to stop your use of your mark after you have invested considerable time and money into it, but could also result in a significant money judgment against you if you generate revenues from your app because of your use of the mark that is similar to the registered mark. Moreover, since you could be deemed to have known about the registered mark since the mark is federally registered and allegedly deliberately chose a similar mark, you could be liable for treble damages.
That said, the international classification scheme is merely an administrative tool of the USPTO and does not mean that every good/service in that class is related and in the same channel of trade. So you should consult with a trademark attorney to determine if your app with your proposed mark could coexist with the registered mark. Chances are, however, that you are better off just selecting a different mark and starting off with a clean slate and no or more minimal risk. It really is not a good idea to get "married to" a particular mark until you know the mark is available.
*Please note my disclaimer in my bio.

The short answer is "It depends". In many countries a registration of a mark can effectively block the entire class; the United States takes a much more granular approach when evaluating likelihood of confusion. A full analysis needs to be determined between the anticipating mark and the proposed mark as mentioned in the earlier post. From a registrability view point, the USPTO evaluates likelihood of confusion using its factors, while the District Courts, depending upon the circuit, use other factors in making the analysis.
As suggested in the first response, the situation needs to be evaluated to make a determination of the relative risks associated.
For a start-up company, the last thing that you want to do is walk into an infringement situation -- it will cost your company a bunch of time, and money, diverting important resources to something that is usually unproductive. I suggest that you consult with an attorney to discuss the specific details. Please feel free to contact me directly with details of the circumstances and i would be happy to look at the situation for you.
Gordon