Okay, but correct me if I'm wrong.
If I were to strip away all of the keys, and knobs, sliders, dials, software, interfaces, and LED displays and get down to the most basic functionality I'd find either a sampler, synthesizer, or both... and note that when I use the word 'synthesizer' I'm referring to a device that makes analog sound using electronics (or a computer model) in much the same sense that a theremin makes analog sound... 'off the cuff' and perhaps never heard by man or beast before. And note that not everything that is called a 'synthesizer' creates analog sound 'off the cuff' as near as I can figure out.
When it comes to samplers there appear to be two kinds... those that reference samples stored internally, and those that reference samples stored externally. And of course both. Keyboards that only reference sounds externally are called keyboard controllers (I use B&H's retail labels here), tend to be the cheapest (in both cost and quality), require a computer (with samples), and are the easiest to understand as to the functionality they offer. Let's ignore them.
I'm also going to cut analog synths off at the knees here. The sounds possible with a hardware synth can also (near as I can figure out) be crafted with a software synth (since every hardware synth nowadays appears to be basically a computer). Which... if true... kind of begs the question how in the heck does the Minimoog stay in the marketplace. But I digress.
So now I'm down to samplers with internal samples, a.k.a. 'arranger keyboards', 'digital/stage pianos', and 'sampling workstations'.
The only significant difference between 'arranger keyboards'/'sampling workstations' and 'digital/stage pianos' is (IMO) the triggers provided. Digital pianos don't have all the bells and whistles, the pads, faders, dials, etc. found on the former devices. 'Digital pianos' also seem to be lacking some software functionality offered in the other devices. But this is not to say that you can't play drums, or brass, or strings, et. al. using a 'digital piano'... just that you have to use the keyboard. And I appreciate that 'arranger keyboards' and 'sampling workstations' have specific functionality aimed at specific market segments. But from a high enough level it's six of one, half a dozen of the other as far as I can tell.
Keyboards... the actual physical black and white elongated thingies... have vastly different levels of quality. In terms of maximum bang-for-the-buck 'digital pianos' rule the roost here. If you want 'graded hammer action' in an 'arranger keyboard' or a 'synthesizer' it comes at a higher price point then in 'digital pianos'. Likewise 'high polyphony' (defined here as 128 voice polyphony or greater) is available at a lower price point in a 'digital piano' then in other keyboards.
So here I am, on a budget, more then a little frazzled, staring at the Casio PX-350 'digital piano'. It has 88 keys (expected in 'digital pianos' but something that kicks the price up significantly elsewhere), graded hammer action, 128 voice polyphony, MIDI I/O, USB connectivity, can function as a MIDI controller (a.k.a. keyboard controller), and costs $750.
To get that functionality in an 'arranger keyboard' I'd be dropping $2,200 for a Korg Pa588 (the only 88 key 'arranger keyboard'
B&H carries) or $2,400 for
a Yamaha S90 XS 88 Key Hammer Action Performance Workstation Keyboard.
I'm thinking if I want to get the functionality that the more expensive keyboards offer I'll just pop for a $600 Nativ
e Instruments MASCHINE and use the $1K I'm saving for a pair of Adam A5X monitors... eventually.