Functionally for passenger? It isn't much different since taxi hailing apps now exist.
For driver, very different. Taxi vehicles are typically exclusive business use, often times used by different drivers in shifts. Different municipalities may set fare rates or minimums for service. May set caps on number of cars. Or might not, maybe they just require commercial insurance and an application to be filled out. It's different everywhere. Some cities lyft/uber drivers are even employees of a subsidiary since not recognized as contractors.
Generally lyft/uber went into markets going 'nananana, we are not a taxi because this is a cellphone! Look at the app! Rideshare!' So regulators ended up having to make a new legal class of service. The companies could just throw straps at the problem until enough users jumped on and 'transit proposals' could be made to towns.
There are certain key differences, but basically the supply of drivers / vehicles, and the pricepoints are regulated by the company rather than by municipal legislative.
Which has upsides and downsides wrt quality, availability, wait time, and pricing, including potential to apply "surge pricing".
For example, municipal yellow cab taxis are known for both being legally obliged to pick up passengers in all relevant areas, and at the same time unwilling to do so in certain areas, due to unprofitability, or perceived risks.
Because its much better, and so attracts more people to the service.
Uber has a great potential to be used as public transport, with dynamic route pathing based on supply and demand. Something traditional public transport could never do.
Traditional public transport certainly could do that (and demand-response routes are a thing in rural places), but fixed-route consistent routes make more sense in urban areas from geometric considerations (and you know, not requiring a charged smart phone to get from point A to B).
Uber is a disaster as public transit. It's functionally little different than just having everyone drive themselves. Not needing parking is a big benefit, but it's still a bad idea.
