There are two main ways to play different sounds on a keyboard: layers and splits.
A layer is when you play more than one sound at the same time. For example, you could play a piano sound and a string sound together.
Layers could be velocity sensitive; depending on how hard you play, different sounds are heard. For example, my keyboard has an orchestral sound. If I play softly, I get woodwinds. Slightly harder, and the strings come in. Even harder, and the brass show up. And if I really give it a whack, the timpani come in at the low end. This uses both velocity sensitive layers, and some splits.
A split is when you play different sounds in different parts of the keyboard. For example, a bass sound in the left hand, and an electric piano in the right.
Splits are almost always defined with a split point. Above that point, one sound is used, and below it another is used. Sometimes you can have gradual split points; The sounds fade into each other over several keys. Some keyboards allow you to set split points anywhere. Others restrict you to certain predefined locations.
Different manufacturers sometimes use different terms to describe this functionality.
So, to play two different parts with different sounds, you need splits. Many, many keyboards have this capability. You also need the ability to transpose each sound separately. This is also quite common.
Generally speaking, there are a few different types of keyboard:
- Workstations have many features, and will easily support most kinds of layering, splitting, and transposition. They have a wide range of sounds. The user interfaces often are a bit quirky. To put it nicely.
- Stage pianos. This is not a great name, but there's a whole class of keyboards like the Nord Stage and Korg Grandstage that are not quite a workstation, but are significantly more powerful than a digital piano. They are designed for ease of use during live performance, and will support splitting and layering. There are likely to be less options than a workstation.
- Digital pianos are more focused on just being a piano. They are less likely to have voice-specific transposition. Most will still have split points.
- MIDI controllers have no brains at all; you run a program on your computer to generate sound. Any software platform that's worth using will support all kinds of layering and splitting. It's possible to use almost any keyboard as a MIDI controller these days.
- Analog or virtual analog synthesisers not support any of these features at all. Neither will many "vintage" keyboards. Actual vintage, or modern-reproduction-vintage.
- Arranger keyboards are designed to play along with you. They will often support all sorts of splitting and layering.
There are probably other subcategories. In general, you probably require a workstation, stage piano, or midi controller of some sort. As there are many possible options, you will need to decide how many parts you need to play at once, and how complicated the splits and layers need to be. There are also many other tradeoffs; sound quality, weight, ruggedness, aesthetics, etc. Those are outside the scope of this question (and probably this site).