Application
also: app, apps, applications
A piece of software built for people to use to get something done, like a banking app, a recipe website or a to-do list.
A program, or a set of programs working together, designed for end users to accomplish tasks. Web applications run in a browser, mobile applications on phones, and desktop applications on computers.
"Vehicles" is the general word, like software. An application is one specific vehicle, like a delivery van: built for a particular job and used by real people every day.
When you talk to your agent about "the app", it assumes one specific application with its own code and settings. Being clear about which app, and what it is for, keeps the agent from guessing.
Your application has two parts: the booking page customers see and an admin page for you. I'll start with the booking page.
Build a simple application where members of my running club log their weekly miles and see a leaderboard. Keep it to one page for now.
Thinking an application has to be downloaded from an app store. A website you use to do something, like booking a haircut, is also an application.