The way I see it is this. I'm going to be using the time travel logic presented in Marvel's "Loki" and "What If...?" as reference.
Loki is where we get our first proper introduction to the multiverse in the MCU. In Loki the TVA monitors "Variant Timelines." Now the term variant can mean either parallel or alternative depending on context.
Let's talk about one single universe, it's singular timeline. In Endgame the time travel logic is this. When something changes it doesn't change the timeline but creates a "branching" timeline, like a branch in a tree. The branch is an ALTERNATE variant timeline, in which they coexist as a part of the same universe, a branch of the same tree.
Then there are PARALLEL variant timelines, or an entirely different, separate timeline with its own alternate timelines or "branches," a separate tree.
Alternate universe in this context means a branch in a tree, and parallel means an entirely different tree.
The Multiverse in the MCU is like a forest, each tree (parallel universe/timeline) has branches (alternate universe/branches/"branching timeline")
The terms are used interchangeably since many don't really see the distinctions, which is understandable. I thought this analogy would help to better understand the distinction.