Honestly had to look it up myself, and I remain confused.

I’m in California, but they didn’t teach us California criminal law.
So what I can tell you based on what I found is that the section you’ve quoted there isn’t the crime of first degree murder, but rather the crime of murder in general. It is section 189 that defines whether a crime meeting the definition of murder is first degree or second degree. First degree murder is murder that meets any of the criteria outlined in that section (of which there are several). Second degree murder is defined as all other murders. So, “murder with malice” doesn’t seem to be a lower charge from first degree murder, it’s just an umbrella charge.
What I don’t know is what this would look like in those jail records that have been posted. You can see that both RH and JH have charges for violating 187. The one that specifies first degree murder for Rebecca still just references 187, not 189(a).
I think we need to see the criminal complaint to know for sure what degree of murder they’re each charged with. Does anyone have the PDF? There’s no copyright issue with those so we should be able to copy them here in full.