Fire Journal is an iOS application, or app. It doesn't need a browser to run. Some software applications look like they are designed for tablet devices, but require Internet access to operate.
Fire Journal is a "local" or "native" app, meaning it will run perfectly without any connectivity to the Internet nor does it require a web browser. Certain functions will not work without Internet connectivity, such as auto-population of an address in a report, journal entry, or form. However, you as the user always have manual control to add whatever you need.
When you subscribe to Fire Journal Cloud, you get all of the functionality of Fire Journal, plus additional reporting and advanced capabilities - and you may access the Cloud app via any modern web browser - Mac or PC.