You may have used an "arranger keyboard" without knowing what that product category is. An arranger keyboard is designed to provide automatic accompaniment--backing tracks--at the touch of a button, in many different styles. Common low-end keyboards fall into this category, like the Yamaha PSR series and the Casiotone series. You may have one, or you may have purchased one for your children. There are also much more expensive, high-end keyboards in this category, like the Genos.
The simplest way to use the accompaniment is to trigger it from the left hand with a keyboard split. Here's what that looks like:
https://www.youtube.com/watch?v=MWW9tyB__3o&t=706
The general two purposes for arranger keyboards is (1) to let you perform as a solo act and (2) make it easier to write songs.
The other three common types of keyboards are synthesizers, stage pianos, and keyboard controllers.
Supposed to be the flagship product, I find very interesting how musical instruments manufacturers carefully differentiate the features between arrangers and workstations.
There is feature differentiation, sure. But I think the biggest difference between product lines is the controls. Arranger keyboards need convenient buttons for changing song sections. Synthesizers need dedicated controls for sound design. Stage pianos have dedicated buttons for the common sounds—acoustic piano, electric piano, and electric organ.
If there is a keyboard that “does it all”, I’d guess that it’s something like the Genos. It costs a couple grand more than the Montage.
To my knowledge there is no clear distinction between arranger keyboards and some more advanced home keyboards. For software, Korg had released their arranger wave-sequencing engine as a plugin. Yamaha has their cheapest hardware board Yamaha PSS-A50.
There’s noodling for fun too.
They can produce a lot of music like sound for not much effort.
You’re one button away a from bossa nova drum track.
A commercial software to generate backing music that my teacher recommended for training jazz improvisation.
The performance was okay. I found it too sterile. It didn’t really swing … especially for the target audience of jazz musicians. It was helpful though!
Judging from its look and feel, Band-in-a-Box is around since the 90s.
I messed around with JJazzLab a few months ago, and, while I did encounter some annoying MIDI problems involving the drum patches, I liked it enough that I wrote myself a script to import a song from another program, Impro-Visor, for auditioning in JJazzLab. It's a lot easier to use than Band in a Box.
Take a look at Yamaha's QY series.
The QY10 can be found for under $100.
Tutorial, https://www.youtube.com/watch?v=d5i66uPOe8g
The QY300 for under $200.
Tutorial, https://www.youtube.com/watch?v=SsR2UX3axNM
As a bonus the dawless approach also generates tones.