The words are used completely differently, and would never be interchangeable. It would be impolite and rare to call a person “submissive“ unless you were talking about a sexual situation. It can be an adjective or noun. It is a sexual term when used as a noun on a person “Submissive” can be used for animals, however. “Pushover” often isn’t used in a negative way, or only mildly. It’s used for a person who can be persuaded to do something or to agree with others. “I’m sure I’ll be able to talk my Dad into driving us. He’s a pushover when it comes to doing things for his only daughter.” “My wife always gets stuck staying late at work to finish some project. I wish she wasn’t such a pushover and would start coming home on time.”

"Submissive" is standard English. It is good, written, formal English. "A pushover" is colloquial, informal, conversational. It's not slang. You could use it when writing informally. You would not use it when writing a psychology paper. They are almost synonymous. (As others have noted, "submissive" is usually an adjective, "pushover" is a noun). To me, a person is "submissive" when they voluntarily choose to obey someone else. They do so willingly. A person is a "pushover" when they are easily dominated. They do not begin by choosing to obey. However, it is easy for someone else to change their mind. "Pushover" also suggests that the dominant person coaxes in a friendly way, rather than threatening or bullying. A "pushover" is "talked into" agreeing. Grandfather: "No! You may not have a second helping of ice cream. One is enough." Child: "Aw, please, please! I've been really good today. I wuv you, Grampy! Please, please!" Grandfather: "Oh, well, OK, I guess." Grandmother: "Oh, Dan! You're such a pushover." The grandfather gave in too easily. Grandfather was a "pushover." We probably would not say Grandfather was "submissive."

I would add that they are different parts of speech. 'Submissive' is an adjective eg a submissive person, whereas 'pushover' is a noun eg that person is a pushover.

You're right, and submissive is usually an adjective, while pushover is a noun.