These people already answered your q's but hell i'll answer anyways.. lol
Midi keyboard= A keyboard used to control other other hardware (other keyboards, modules, tone generators) or software (fl studio, reason, etc).
It creates NO sound of its own, just used to control other sources of sound.
Synthesizer= Sound creating hardware attached to a keyboard for the most part.. some synths have non keyboard versions, called rackmount synths, synth module or whatever they would call em.. Also some (probably most) synths are Midi keyboards themselves, if they have midi ports or USB-midi.
Imo i would buy a synthesizer with midi as a first keyboard, so you can have fun with the hardware (i'm just hardware biased) and use it as a midi controller when needed, and buy midi keyboards as your own personal studio gradually develops. But then you say you just want to sequence with DAWs, so i guess getting a cheaper midi keyboard is the better idea for you..