The short answer
A website tells people about your business. A web app lets people do work with your business: book, order, apply, track, approve, report. If people mostly read, you need a website. If they log in and get things done, you need a web app.
What a website is for
A website presents who you are, what you offer and how to reach you. It is mostly the same for every visitor, it is updated by your team from time to time, and success is measured in visits, enquiries and calls.
What a web app is for
A web app runs part of your business. People sign in, enter information and get results: an order system, a booking calendar, a staff portal, an insurance quote, a job board. It stores data, follows your business rules and often connects to other systems such as accounting or payments.
Signs you have outgrown a website
Staff copy the same information between spreadsheets and email. Customers phone to ask about things a screen could tell them. Approvals live in WhatsApp threads. Reports take a day to put together. Each of these is work a web app can take off your team.
You can start with one and grow into the other
Many businesses start with a strong website and add web app features as they grow: a client portal, an online form that feeds straight into your system, a dashboard for managers. Building on the right foundation from the start makes that growth cheaper.
How to decide
Write down the three tasks that cost your team the most time each week. If any of them involves people entering or looking up information, that is a web app problem. Bring that list to a conversation with a developer and ask what it would take to automate the first one.