Electrical – Is it safe to touch a running 1 hp electric motor

It boils down to current distribution, but let's start from the beginning.

In both cases you form a circuit with several elements in series. Some of them have excellent conductivity, like copper wires. You are of meager conductivity, but your shoes and ceramic tiles have even worse conductivity, they are dielectrics. As the dielectrics have contact to or are in between conducting elements in a geometric relationship they form capacitors. This circuit consisting of capacitors and resistors permit AC current to flow. Aside from some other effects the current should be the same order of magnitude in both configurations.

What's the difference now between both cases? When touching the copper wire you form a conductive connection with a very small area for the carriers to pass. As two conductors connect, there can't be a strong electric field either. Due to the small area the current density maximises and you can sense it. n.b.: you can't sense it at your feet, can you?

The other case differs as you touch a dielectric. This dielectric differs from the surrounding air but not very much to change the electric field dramatically. Hence the electric field vectors connect to your skin perpendicular and with merely unchanged field strength. At your skin the electrical surface charge influenced by the field causes a current, but this time distributed over the surface of your hand. You can't sense it.

The wire gauge required by the NEC is determined by the circuit breaker protecting the branch. In the case of a short, even in a low current branch, the wire conductors need to be able to handle the momentary over-current of the short. If the short is not "perfect", the breaker will happily supply 60 Amps+ into it for an indefinite period of time. Not a good situation if the conductors are sized to carry 2.5 amps (presumably #14 wire, the smallest permissible gauge for branch circuits). For safety all branches of the circuit are assumed in the NEC regs to be able to carry the amperage dictated by the circuit breaker serving that branch.

By the way, if you have "long" cable runs to the high amperage motor you may find that the motor is starved for starting current due to the round-trip resistance of the conductors. This resistance may create a voltage drop in the wires sufficient to prevent the motor from starting, or cause it to start slowly or erratically. In your specific case you have that 25 Amp heater complicating matters. If the heater is also on the same long branch of the circuit, it will create its own voltage drop in the wiring which will affect the voltage available to the motor when it starts. In these cases you will need to use a heavier gauge cable than is dictated by the normal ratings of the motor.