Using Topsy when you do not have a smartphone handy
The website does the whole booking. No install required.
A persistent assumption about ride platforms is that you need the app. For Topsy you do not: the website carries the full booking flow, and there are several situations where that is the better option.
What the website does
Price a route across every available ride class, book it, pay for it, and track it. Schedule a trip for later. Book for somebody else with their name and number on the trip. Manage a Topsy Teens arrangement. Send a parcel and follow it.
That is most of what most people need.
When the website is genuinely better
On a laptop at work, arranging travel for a visitor or a colleague. Booking from a borrowed device. Setting up a recurring school run, which involves enough fields that a keyboard helps. Arranging travel for somebody who does not use apps.
What the app adds
Food, Market and Medicine ordering are in the app rather than on the website. So is attaching a flight reference to an airport booking, where the website uses the notes field instead. Push notifications for trip updates are an app feature, and for a trip you are actively waiting on they are genuinely useful.
Tracking without an account
Worth repeating because it surprises people: a shared trip link works for someone with no account and no app. If you are booking for a relative, they can watch the car arrive on whatever phone they have.
Delivery tracking works the same way, which is what makes Send usable for a recipient who has never heard of Topsy.
The practical answer
Use the website when you are at a computer or on someone else's device, and the app when you are out and want notifications. There is one account behind both, and a trip booked on one appears on the other.