Can I say something like:
- Please note that the ocean is pink.
- Please notice that the elephant is small.
Which is the correct one? Or are both correct? Or wrong?
To notice X is to acknowledge that X is in your sight, hearing, etc.
To note X means that X is important and you should remember it. If you have a physical notebook it can mean to actually write X down.
You may be expected to specifically recall something you noted or that someone asked you to note, whereas notice is more used to just "keep something in mind."
If something is really important, a speaker or writer may use note over notice for emphasis and vice versa.
These two terms are incorrectly used interchangeably when there is actually a significant difference between them.
"Please notice X" is used to draw someone's immediate attention to something which is often a sensory or perceptual effect. You are guiding the viewer's perception to something in particular. A tour guide might say "Please notice the design of this building", inviting the viewers' gaze to the building so that he might point out something of interest about it.
"Please note X" is used to tell somebody that they should make a conscious effort to remember the piece of information X because it is somehow important. It is less to do with immediate sensory/perceptual information and more to do with committing something to memory (for whatever reason).
Note comes (indirectly) from Latin meaning “mark” (as in write down), and notice also from Latin meaning something like “know this”. The latter came to mean something printed in the 19th century.
Modern usage often conflates the two; the meanings are closely connected, the chief difference being that a “note” is a physical record of something, but “knowing” relates to awareness of that thing.
Think “words” versus “information”.
They are synonyms. "Please note" is more common.
In the context of giving some useful advice or recommendation, to me, to note something is to notice and remember it as something important.