What does "gazed out over" mean?
Hi, what does "gazed out over" mean? Has gazed out over same meaning with gazed out on? Thanks.

(gaze out on)
gaze out on something
to look out on something, such as a lovely view, from inside a building or from a particular spot. She gazed out on the flowering trees and knew that life would go on. Henry sat for hours, gazing out on the lake.

Context :

Lisa [gazed out over] the Caribbean Sea, feeling the faint breeze against her face - eyes shut, the white sand warm between her bare toes. The place was beautiful beyond belief, but it was still unable to ease the grief she felt as she remembered the last time she had been here.

Question

What does "gazed out over" mean?
Hi, what does "gazed out over" mean? Has gazed out over same meaning with gazed out on? Thanks.

(gaze out on)
gaze out on something
to look out on something, such as a lovely view, from inside a building or from a particular spot. She gazed out on the flowering trees and knew that life would go on. Henry sat for hours, gazing out on the lake.

Context :

Lisa [gazed out over] the Caribbean Sea, feeling the faint breeze against her face - eyes shut, the white sand warm between her bare toes. The place was beautiful beyond belief, but it was still unable to ease the grief she felt as she remembered the last time she had been here.

Answer

Yes it really means the same as "gazed out on", except gazed out on suggests, to me, looking at something specific, such as flowering trees.

To me "gazed out over" sounds like not looking at anything specific. Gazing out over the Caribbean Sea would mean looking out to the horizon or any other non-specific point, thinking about "the grief she felt as she remembered the last time she had been here" and not thinking about anything that can be seen.