I would also like to know

Yes it's all of the above depending on mode and options. If you want an increasing puzzle challenge then the game has a rush hour mode, that keeps throwing more and more trains at you each level.

Although I am still in the tutorial, there are essentially three different game modes: endless, time table, and rush hour. In the endless (aka sandbox) mode, you build your train network from scratch with you just starting with a limited amount of currency, a few train stations and an sparse train rail layout. However, you have to prove yourself worthy by scheduling train routes and having them arrive on time before you can unlock the additional technologies of your choice. The overall objective is to have a minimum number of commuter, freight and / or regional trains operating on or ahead of schedule during a hour time interval. Your star rating is based on how far you have progress your green (commuter) and red (freight and regional) rail technologies. Your leader-board ranking is based on the combined on-time arrives of all your trains across your train network in the one hour time period.

In the time table mode, your train stations, rail layout and operation schedule have been predetermined. To further progress your objectives, you have to successfully have the specified number of trains arrive on schedule. This is slightly more difficult than the endless mode since you are not the one choosing the schedule that the trains must follow between the various train stations. But, if I recall correctly, you do get to design the train rail layout using the limited technology that you have available. In this mode, your star rating is based on the number of trains that reached their destinations successfully as scheduled.

Rush hour mode is probably the most complex of the three since you have to design, build and maintain your train rail network as multiple waves of commuter, freight and / or regional trains operate across your city. As you progress through the rush hour phases, you will unlock additional technologies to utilise in your rail network hopefully being able to make it more efficient. This mode is both scored based on your performance and timed -- your leader-board ranking is based on your overall score; however, the your time is also displayed.

Note that for each game mode there are multiple city maps from which you can choose and some are more difficult than others. Furthermore, even though the same city may be chosen for the different game modes, the objectives, number of train stations, difficulty, etc. can and will be different. Depending on the game mode, there are a minimum of eight to over twenty city maps created by the developers and several dozen to over a thousand city maps created by the mod.io / steam community.

While they are a year old, Master Hellish has a set of tutorial videos that will introduce you to the basic game play of all three game modes.

https://www.youtube.com/watch?v=DZhhHzb6y9Q&list=PLX9TPVcxrORNdCtMUTsOcJ-ob1fepzOAm