You're assigning a rigidity to these terms that they simply don't have. A "console", in the oldest sense of the term, is any place where a user interfaces with a computer, or more broadly with any kind of machine.
>Borrowed from French console (“bracket”, noun), from consoler (“to console, to comfort”, verb). Sense of “bracket” either due to a bracket alleviating the load, or due to brackets being decorated with the Christian figure of a consolateur (“consoler”), itself perhaps a pun on the first sense (alleviating load). Originally used for the bracket itself, then for wall-mounted tables (mounted with a bracket), then for free-standing tables placed against a wall. Use for control system dates at least to 1880s for an “organ console”; use for electrical or electronic control systems dates at least to 1930s in radio, television, and system control, particularly as “mixer console” or “control console”, attached to an equipment rack.
A "terminal" is a text-only console. For a long time, "terminal" and "console" were synonymous. By metaphor, in the same way that a "desktop" is not a desktop, referring to a terminal emulator as a console is perfectly acceptable, and everyone will understand what is meant.