My 2 cents
I've been wandering around the site for a while figure I might drop a few opinions off here.
By psychological definition a masochist is one who derives pleasure from having pain and/or humiliation inflicted upon them. This can be in many forms from actual physical pain to, as you stated, being forced to do something and being humiliated in doing so.
The way you stated your question somewhat confused me and I'm guessing what you're asking is the difference between Dom/masochist vs. Dom/sub. I guess the easiest way to explain it, or how I see it in my life and experiences, is to not refer to is as Dom in both situations. Sadist/masochist and Dom/sub work better.
In S/m you have one who likes to inflict pain and humiliation and one who likes to receive it. This can boil down into even vanilla relationships as a simple slap on the ass while having sex or pulling hair and can be as intricate as your imagination and the physical limitations of the masochist can handle. Also in S/m it tends to end when the session ends and that's the extent of it.
In D/s it's more of a power transfer while most subs would be considered masochistic it wouldn't be the driving force of the relationship. Unlike S/m relationships someone in D/s would be more likely to retain the role for a longer period of time as it's part of who they are to serve the person out of fear and respect rather than to seek some physical pleasure. Granted subs usually get physical pleasure in some way out of the serving and I as a Dom usually give a reward as well when I am pleased, however, the ultimate reason for the actions is not to gain pleasure from the humiliation of the act as to a sub it is not humiliating to serve it is an honour to serve their Dom.
Ultimately it comes down to masochism is more of a pleasure seeking side of things, almost like a fetish, whereas, submission is more of an attitude and personality that makes the person feel as if they are doing something for a purpose not to gain pleasure.
Correct me if you see things differently and sorry if I misinterpreted the question I was confused by the wording. Hope this helped.