≈ vs. ~ --- Which symbol is more correct to use?

FYI from Wikipedia regarding the tilde (~) I think most people use ~ just one, because it is available on the keyboard.

This symbol (in English) informally[4] means "approximately", "about", or "around", such as "~30 minutes before", meaning "approximately 30 minutes before".[5][6] It can mean "similar to",[7] including "of the same order of magnitude as",[4] such as: "x ~ y" meaning that x and y are of the same order of magnitude. Another approximation symbol is the double-tilde ≈, meaning "approximately equal to",[5][7][8] the critical difference being the subjective level of accuracy: ≈ indicates a value which can be considered functionally equivalent for a calculation within an acceptable degree of error, whereas ~ is usually used to indicate a larger, possibly significant, degree of error. The tilde is also used to indicate "equal to" or "approximately equal to" by placing it over the " creator" property="author" typeof="Person">ElectricPavlov Feb 14, 2017

For example:

log 4 ≈ 0.477

log 4 ~ 0.477

Which statement is more correct?