In the context of iterative methods for equations and linear systems, one usually says that "linear convergence / order 1" is when the error $err$ goes to zero with the number of iterations $n$ as $err \sim \rho^n$ for a certain $\rho<1$ (e.g., fixed-point method, Jacobi method for linear systems), and "quadratic convergence / order 2" is $err \sim \rho^{2^n}$ (e.g., the Newton method for a simple zero).
On the other hand, in the context of numerical quadrature and methods for ODEs, one usually says that "order 1" is $err \sim \frac{1}{n}$, when $n$ is the number of subdivision points, usually equispaced; (e.g., the explicit/implicit Euler's method), and "order 2" is $err \sim \frac{1}{n^2}$ (e.g., trapezoidal rule).
These two incompatible definitions are also discussed, for instance, on Wikipedia.
What is a good way to differentiate them in teaching to prevent confusion? If possible I would like to avoid introducing non-standard terminology. This is in the context of an undergraduate course in numerical methods.