It turns out you can use some smaller Lego train sets on Brio tracks, which is a great way of combining the two systems, if you have children that want to design and build their own trains.
Lego does produce it's own system of trains and tracks, but these are very expensive. They also make slightly smaller kits (smaller than mini-fig scale), such as the Creator kit Winter Holiday Train 30584. Lego doesn't produce any tracks for this scale of train.
The wheels sets are made out of two parts, the wheel holder (Plate, Modified 2 x 2 with Wheels Holder, Item No: 4600) and the wheels (Train Wheel Small, Hole Notched for Wheels Holder Pin,Item No: 50254). The instructions say to assemble the wheels with the flanges on the inside, this way they don't fit. But if you reverse them, they fit nicely into the grooves of wooden Brio style tracks.
This fits so neatly it almost seems like it could be intentional, even though I suspect it isn't and is just a coincidence of the different scales lining up.
Now your Lego trains have somewhere they can run. Our children were also given a bag of just wheel sets and coupling connectors from a relative (as it turns out Lego will sell you individual parts), and now they can make as many different types of engines and carriages as they can imagine.