In my work "=" is the identity of a number so it states an equivalence.
1=1, 2x=10 ie x =5.
The approximation sign "≈" I use for decimal approximations with tilde "~" being a rougher approximation.
Tilde "~" I use to state a geometric shape is similar to another one ie a triangle of sides 3/4/5 is similar to a triangle with sides 30/40/50. I write ▲ABC ~ ▲A'B'C' where ▲A'B'C' is a dilated version of the pre-image.
For a closer similarity "≃" might mean a triangle almost congruent but only ROUGHLY similar, such as two triangles 3/4/5 and 3.1/4.1/5.1 while "≅" means congruent. Real life triangles use approximations and have rounding errors. 3/4 does not equal 3.1/4.1 but could be rough approximations for something already constructed. As such this is not a popular use and purists and rigorous math profs disdain it because they do not have a way of using it or defining it soundly. That is why laymen or service professionals are free to explore it and academics prefer something more clearly defined unless deformations are allowed as in my case.
Triangle 3/4/5 is ≅ to triangle 4/5/3 the difference being a rotation changing the coordinates of the angles but preserving angle and side length.
Also I use the definition symbol "≡" to define functions. Simplest case is f(x) ≡ y. I am using it to state a relationship to find sums instead of stating it as the sum that we are deriving however it can be used to state equivalence. For a quadratic I would set f(x) to zero but would not define f(x) as zero. I use ≡ for all cases, not only immediate ones. Setting f(x) to zero creates the equivalency f(x) = 0 for the coordinate you are trying to solve but is not true for all coordinates that are solvable.