I am thinking of it as that a high impedance (high Ohm?) input would require a higher current to activate a state change like you mentioned about the TTL . I must be viewing the term "high impedance" from the wrong standpoint.
What you are doing is confusing voltage controlled devices with current controlled.
As was explained, a high impedance device (ex. MOSFET or CMOS) is controlled by voltage levels. A bipolar junction device is a current controlled device. The emitter-collector current is controlled by the base-emitter current. This is how it amplifies a signal, a small current at the B-E shapes a higher current at the E-C.
In a Field effect device, there is a high impedance (resistance) between the gate-source (analogue of base-emitter). When a voltage is present, an electric field occurs. This field redistributes the charge carriers in the P or N material, creating a channel for current flow or closing it off, depending on the voltage and configuration of the device.
It is key to remember that a voltage is potential energy, and a high input impedance creates a potential difference equal to the applied voltage. In FE devices, the potential is nearly infinite, so there is little current draw at the G-S. thusly, a 5 volt signal will switch a typical MOSFET on or off without much current flow from G-S. This makes MOSFETS particularly suited for low power digital circuits.
BJTs work differently. They have a lower input impedance at the B-E junction, similar to a forward biased diode, which is what they really are. This requires a current limiting resistor at the base of the transistor to prevent too much current. A BJT is current controlled in this matter between its cut-in and saturation limits.
Low impedance means more current flowing.
High impedance means voltage controlled.
All of this relates to Ohm's Law.