If a procecuter says "1st degree murder" or something like that and the jury/judge do not agree what happens?

Possible they try for second degree or manslaughter. It depends on if they can all agree that the crime was premeditated.

The prosecutor (DA) will bring charges. The defendant will defend himself or herself. There will be a trial.

@kritiper “Possible they try for second degree or manslaughter.” Would you elaborate on that?

If the suspect doesn’t qualify for first degree, premeditated murder, then possibly second degree, non-premeditated murder, or manslaughter (accidental, non-intentional death) may apply.

@kritiper How exactly would/does that happen procedure-wise?

I suppose the DA determines what the call will be, initially, since he/she is prosecuting the case, based on the evidence collected. Once the trial plays out, it may become apparent that the murder was not pre meditated, the jury would rule that, and a lesser sentence of second degree, or even manslaughter, will be handed down. But usually, the degree of murder is pretty much decided on before the trial starts. All parties concerned are given the same evidence before trial so there usually/rarely (if at all) aren’t any surprises during the trial.
Don’t you ever watch Perry Mason?

Most times the jury has the option of finding guilt of lesser included charges, such as manslaughter or negligent homicide if jury is not convinced that the elements of first degree murder were proven.

How about for example OJ Simpson’s case or
Guy Turcotte’s case: https://nationalpost.com/news/canada/former-quebec-doctor-who-admitted-to-stabbing-his-children-will-be-released-on-bail-judge-rules

…Are those good examples? I’m no longer sure.

@flo: In your link, The judge set him free on bail while he awaits a new trial. He’s not found not guilty.