I recall the difference in the definitions being confusing for most of us kids.
So perhaps rather than just emphasizing the difference between = and ≡ more, it would be better to go further and emphasize the difference between universal and existential quantification more. Quantifiers can be confusing, but I think people also find having two different equals signs confusing; and it wouldn't be necessary to give a full account of predicate logic to high schoolers, I'm thinking more of just informally describing the difference between "for all" and "there exists" and reminding them that a bare variable has no meaning if you don't know what set it ranges over and how it's quantified.
This is just my speculation, I have no experience with mathematical education whatsoever.
Right, I've uni math also formal logic so I've knowledge of universal and existential quantification, etc. thus an understanding of the issues.
You're right, that stuff's a bit too heavy for highschoolers. Perhaps all that's needed is to be told 'that at times these appear the same but later on you'll need to understand there's a mathematical distinction' then emphasize the difference aspect to drive the point home.
Even though it was a long time ago I mostly recall what the teacher said and whilst he gave a few examples he never emphasized that there was a mathematical difference and that it was an important fact to know. Matters became more ambiguous from our science courses, the use of 'equivalent' was very loose.
I reckon the same or similar should apply to other topics, calculus for example.