I'm not sure what you mean by climax/cum. Are you talking about a female ejaculation? The first time for me, I was close to orgasm and ejaculated. It surprised me so much that I lost the urge, so to speak. lol So I do believe you can have one without the other, but I think you have to really, really aroused to ejaculate.

In general the word orgasm and climax describes the same thing and ejaculation or cuming describes the same thing.

For woman the climax and orgasm describes the exact same thing.

Men can ejaculate/cum without orgasm/climax, or orgasm/climax without ejaculating/cuming.