The terms get used almost interchangeably in casual conversation and in a lot of product listings, which makes them genuinely confusing to shop with. There is a real distinction, though it's more about design intent than a hard technical line.
What "vacuum flask" traditionally means
Vacuum flask originally referred to a specific construction: two walls with the air removed from between them, creating the vacuum that slows heat transfer. Historically, and still often today, flasks are associated with hot beverage retention specifically, tea, coffee, soup, and tend to have a narrower mouth and a stopper-style cap rather than a wide drinking opening.
What "insulated bottle" usually means
Insulated bottle is the broader, more modern term, covering the same vacuum-wall technology but applied to a wider range of formats: sports bottles, sippers, wide-mouth designs meant for both hot and cold contents and for drinking directly rather than pouring into a cup first.
Where the line actually is today
In practice, most products marketed as "bottles" now use the same vacuum insulation technology that flasks always have. The meaningful differences left are mouth width (narrow for pouring, wide for drinking or adding ice), cap style, and the use case the product is designed around, not the underlying insulation technology itself.
The short version
If you're comparing two products and one is labeled "flask" and the other "bottle," don't assume one insulates better than the other by default, check the actual construction (double-wall, three-layer, vacuum-sealed) rather than the name on the label.