In general it is quite hard to clearly differentiate trains between intercity and local. Usually biggest difference is made by longer loading times for intercity trains. That is because inside a city center you need as much space effectiveness as you can get, meaning that mainly loading speed, but also train capacity and early acceleration takes precedence over speed and total acceleration trail.
Note: train speeds are in the code values. The in-game values might be a few km/h higher, but they count the curve length speed from the code values so those are the important ones to mention.

Intercity class

Rail intercity

These are the rather normal trains which have amazingly high power and very nice speed. All this while keeping rather high cargo capacity. Their main downside is the severe vulnerability to short curves, therefore they are best used when they are rather short.
Wicked Warp goes 300km/h with TL long curves

Monorail intercity

Similarly to the fast monorail class, these trains also get more powerful with increasing length. This makes them very effective with longer trains if you are able to afford the very long curves.
Maelstrom goes 600km/h with TL long curves

Maglev intercity

As maglev tracks have the curve speed bonus, it is suitable to abuse that with intercity trains. Maglev Intercity is able to go through CL2 or 3 in full speed, while maintaining solid acceleration. Their capacity and loading times are a bit lower and the low capacity of the engine itself makes them unsuitable for local transportation.
Touch of Hate goes 316km/h with CL2
The Day I Die goes 403km/h with CL3

Local class

Rail local

The most classic local trains are very effective for transportation inside city centers and in the busiest areas in towns thanks to their high raw throughput capabilities. They however do suffer from short curves. In order to provide better variety, there are three sub-classes which scale in speed, power and cargo capacity.
Morphogenesis goes 140km/h with CL3 and medium capacity
Timewave Zero goes 120km/h with CL2 and high capacity
Holographic Universe goes 160km/h with CL3 and lower capacity

Monorail local

Monorail local trains are very interesting as they reduce capacity with increasing length, but they also reduce loading stages with increasing length.
Their length does not matter too much normally because they never slow down in curves. This is changed as you can truly choose what stats should the trains have by just using a selected train length.
More capacity or loading speed, the choice is yours!
Apocalypse goes 158km/h through CL1

Maglev local

Maglev trains are able to go through the shortest curves in full speed, but their engine capacity makes them effective only with longer trains. They are best used in suburbs where their lower capacity does not hurt them, but they are able to travel through sharp corners efficiently, and thanks to their high speed they get high station ratings. Due to that utility they can also be considered rather one of the bonus engines with rather low throughput capabilities.
Meat Grinder goes 211km/h through CL1

Other passenger engines

The Doombringer

What else is more badass than a modern black steamer running on dark energy with increased loading speed and in spare time bringing doom? Yes that’s right.
If used on PURR tracks, it gains various bonuses just like other MEOW vehicles.
Can only transport express cargoes.

The Doombringer goes 170km/h through CL4

Destroyer of Worlds

Currently in testing, behaviour likely to change.

The SLUG

While they have extremely low capacity, they load only in 5 loading stages and get all the helpful curve length bonuses, making them considerable for a messy mixed network.
Furthermore, Animal Express travels the same speed as Meat Grinder does - including curve length requirements - but Meat Grinder has considerably higher capacity!

Animal Express goes 211km/h in CL1
The SLUG goes 265km/h through CL1.5

Cargo engines and express cargoes

The cargo engines are in general a compromise between local and intercity in loading speeds, but their capacities tend to get rather low, not to mention lower speed/power compared to the Intercity class.