Different models have different capabilities, so the following comments are intended as general information and might not apply to a given model.
First, most DSP effects are system settings, which means they apply to the entire keyboard system wide rather than just a specific part or voice. In other words, if you were to select a particular type of DSP effect, that same type of effect would be applied to the Right1/Main voice, the Right2/Dual voice, and the Left/Split voice. You can usually set the amount or depth of the effect for each voice-- including a depth of 0, which would turn the effect off for one or more voices-- but you could not select one type of DSP effect for one voice and a different type of DSP effect for a different voice.
To give you more flexibility, some keyboards will have two or more DSP effects, such as DSP1 and DSP2, which lets you select different types of DSP effects for different voices. They are still system wide, but you can set each voice to a different depth. For example, you could set DSP1 to one type of effect and set its depth to 0 on the Left/Split voice, essentially bypassing it on that voice, and set DSP2 to a different type of effect and set its depth to 0 on the Right1/Main voice, bypassing it on that voice. This way you could have DSP1 change the sound of the Right1/Main voice but not the Left/Split voice, and have DSP2 change the sound of the Left/Split voice but not the Right1/Main voice, even though technically both DSP1 and DSP2 are being applied system wide to all voices.
Reverb and chorus are two types of DSP effects which are very commonly used-- so commonly that it's become standard for them to have their own dedicated DSP settings on keyboards. In other words, if your keyboard has a Reverb Type setting, a Chorus Type setting, and a DSP Type setting, those are really DSP1, DSP2, and DSP3, except the Reverb Type setting will be limited to just different types of reverb, the Chorus Type setting will be limited to different types of chorus, and the DSP Type will let you choose from any available type of effect-- including all of the available types of reverb and chorus. Thus, you could use DSP Type as "Reverb Type 2," as "Chorus Type 2," or as some other completely different type of effect.
Some keyboards also have "insertion" effects, which are inserted into the effects chain for just specific voices rather than being applied system wide.