NB: This is an open research problem, and there are several people currently doing research on communicating the security provided by end-to-end encrypted chat applications. So there is no research coming to our rescue here, only design thinking.
Another note: there is no such thing as a security / usability trade-off. There's design principles, constraints related to security, and to that add poor designers and good designers.
You should communicate to your users the level of security they should expect. In this case, a visual approach is what I would recommend.
When you advertise / install / run the app, showing a visualisation of two people communicating over a secure channel (and possibly third-parties failing to pierce through the channel) could help users conceptualise that they are talking peer-to-peer and securely.
When people switch to the Web view, it should be prominently displayed this time that the messages transit through a server that is branded with your company's brand identity, and you should show that this server is able to read / intercept messages (depending on what your solution actually does).
Why visualisations? The idea is to rely on the human ability to process spatial concepts without rationalising them. By showing the boundaries between users, the branded server, and external parties, you can communicate the provided security effortlessly. See Dourish's 'Where the Action is: The Foundations of Embodied Interaction' for a (long) explanation of why this might ease your users' task of sense-making.
You should also clearly communicate the risks associated with signing up / exchanging identities on your system if any. It seems from your succinct presentation of your product that there are many aspects that have not been thought out at all.
As the task is daunting, I extremely strongly recommend hiring designers. Specifically, an interaction / service / information experience designer to take care of the presentation of the tool's benefits and limits and the general security interactions; and a graphic or motion designer to work on whatever security visualisations you might end up wanting.