People ask for a website when what they actually need is a tool. The two get quoted, built and budgeted very differently, so it is worth knowing which one you are asking for before anyone starts.
The difference in one line
A website tells people things. A web app lets people do things. A brochure site explains your service and invites an enquiry. A web app takes an input, does something useful with it, and gives something back, and usually remembers what happened.
Signs you need a web app, not a website
The clearest sign is a spreadsheet doing a job it was never meant to do, passed between people, held together with colour-coding and hope. Others: someone rekeying the same information into two systems, a process that only works because one person knows the steps, a form that generates a pile of emails somebody sorts by hand, or a service you would like to offer but cannot, because it would not scale past ten customers.
If any of those sound familiar, the answer is not more pages. It is a small piece of software that does the repetitive part properly.
Why the distinction matters to your budget
A website is largely design and content, and the cost tracks how much of each you need. A web app is logic, data and edge cases, and most of the cost sits in the bits nobody sees: what happens when two people do the same thing at once, what happens when the data is wrong, who is allowed to see what. That is why a five-page site and a seemingly simple tool can be worlds apart on price, and why a vague brief for one gets quoted like the other.
You often need less than you think
The instinct is to specify a big system. Usually the honest answer is a small tool that does the one painful thing well, and leaves everything else alone. Smaller is cheaper, faster and far more likely to be used, and you can always extend it once you know it works.
The question worth asking first
Before anyone quotes anything, ask what the actual job is. Not what the thing should be, but what has to change. If the answer is that people need to understand something, you want a website. If the answer is that people need to do something, repeatedly, without it falling over, you want a web app. We build both, and the first thing we do on any brief is work out which one you genuinely need.