Dynamo generators will motor, when connected to a DC supply and supply DC output. Alternator generators will not motor and produce an alternating output. They are all generators but either DC or AC.
Dynamos are, therefore ‘driven motors’ (look at the name). Obviously designed to generate rather than motor, but basically of the same form. They have commutators and need brush gear whereas the alternator generator has slip-rings and brushes. Remember, too, that commutator motors will operate with either a DC or AC supply.
As far as I am aware, all dynamos are armature-wound (for the output), but alternators may be armature- or stator-wound for the output. Vehicle alternators are all stator-wound, these days. Most alternating generators, which are required for a DC output, are three phase (or more) machines which will deliver a DC output (after rectification) with much less ripple than possible with a single phase output.
Armature wound alternators are less common these days but have certain advantages over stator wound versions. Weight is not usually one of those as the frame is often basically a rolled steel magnet, but starting inductive loads is a definite advantage over the stator-wound offerings with electronic voltage regulation.