Why is it important to point out that Santa Monica isn't the same as the city of Los Angeles? If you live there, you probably know already. If you don't live there, it doesn't matter anyway. They're neighbors. And it's not like Santa Monica is any more culturally unique than the dozens of communities that make up L.A. proper.
Living in LA could mean anything from Brentwood or Bel Air (which I'd strongly argue are not bad places to live) to ghettos in South Central. Most people speak in terms of neighborhoods in LA, and most people consider Santa Monica a kind of neighborhood in LA even though it's a separate city.
Like if I say I live in Marina Del Rey and I have a friend in Santa Monica invite me over, it's not a big deal. That's what important. If I live in SF and a friend in San Jose invites me over, I'm like hmmm do I really want to drive an hour..
Thats like saying living in the tenderloin is a kind of bad place to live but noe valley is not. Both are in SF just like both Santa Monica and downtown LA are considered part of the same "greater LA"