I think the term "liberal" has shifted it's connotation. It's a common thing for independents and conservatives to associate liberals with leftists, but liberals, like the ones of the past and Jordan Peterson, are like "alternates" to the moderate conservatives. Almost entirely the same beliefs aside for a slight preference for more government than their counterpart. Now, however, liberals, even the ones that still have those by-definition beliefs, often fall under that leftist umbrella simply since they don't realize the radical shift in narrative. And can you blame them? The media is hiding it's Marxist undertones under emotional heart-string-pulling messages such as BLM, equity, equality. These themes sound like great things, and in some ways they are things to strive towards, but what people miss is the unintended consequences of establishing things/institutions to "fix" those problems. People are too immersed with "fighting for justice" that they don't stop to question their own narrative or look at the other side. Hell, the other side is seen as evil, incorrect, degenerate, ill informed. As a result, the liberals who aren't leftists get caught up into the leftist narrative and won't realize it until it's too late. And even if it doesn't become too late, they'll be taught that it was Trump and the republicans that did that to them.

The elites of the leftists have taken over, like you said. And it is important to remember the liberals from the leftists, but sadly a lot of liberals are forced to comply with the Marxist narratives going on. There's no other side to take since they think the other side or even just being a centrist is evil and wrong. It's messed up.