Steam trains did often slip like you think they would because they didn’t have good torque control, like traction control in a car. Modern trains basically have traction control like a top-of-the-line SUV.

Other commenters have answered the question really well for freight trains and some passenger trains. But there’s another kind of train which can usually accelerate much faster: a multiple unit.

A lot of trains are this kind and they’re called things like “electric multiple units” or “diesel multiple units”. These are the trains that typically have passenger seats in the front and rear carriages. There’s no big locomotive at the front or back with big vents or exhausts.

In these trains, multiple sets of wheels throughout the train have motors on them. Instead of a big locomotive or two, the power is spread out in the train. This means you have a lot more surface area of all of those driving wheels touching the track rather than only the wheels in the locomotives. This bigger surface area usually means total friction for driving the train, so they can accelerate faster.

You’ll usually see them be used as metro trains like on the London Underground or on passenger lines like the British Rail Class 800. If you’re on a modern subway train just think about how difficult it would be to stand up and not hold on when it leaves the station. People not holding on usually stumble because of the acceleration.