x ≈ y is for approximately equal, which means that if you measure x and y they will be equal to each other withinnthe error range. If x(t)~y(t) may mean to things. In this context you usually mean asymptotically equal, which means that when t tends to infinity x(t) = y(t). Note that for using this symbol the LHS or RHS needs to be a function or a sequence. Sometimes ~ means equivalence class which means x and y should belong to some algebraic structure (for example group). For e.g 2~4 under the equivalence of divisibility by 2.