You are fighting with a mix of old and new terms. A sequencer used to just record, manipulate and replay MIDI - in from a keyboard, then out to a variety of other keyboards, synths and samplers. Nobody called them digital workstations. Then (using Cubase for me) the latest version recorded MIDI and Audio - audio in from the sound card, then via the sound card, out again. I had 16 channels of digital audio from two 8 channel Soundscape cards - and at first it recorded and played - then did some eq, then sends, using the 16 in and 16 out - so you used your old fashioned analogue interface. Then they started making plug-ins and you could do stuff inside the computer. My cubase system is still a sequencer, it's now a DAW too, and probably a recorder, although I've never called it that. If you buy a modern workstation, you can do it however you like.
As for keyboards that record - my Korg does it. It has a record button, and apparently I can even plug a mic into it. No idea how it works because Cubase does all these things better. None of my kind of audio recording and editing would be possible on a keyboard.