In the English language an orbit is:
orbit noun (2)
Definition of orbit (Entry 2 of 3)
1a: a path described by one body in its revolution about another (as by the earth about the sun or by an electron about an atomic nucleus)
also : one complete revolution of a body describing such a path
b: a circular path
Note that the definition says nothing about the physical forces creating the orbital path of the object.
In astronomy and astronautics, an object in a orbit is moved by a combination of the gravitational forces on it and its initial velocity. If a spacecraft is given a high enough orbit around a planet by its initial orbital insertion it can stay in orbit for years, decades, centuries, millennia, or even millions or billions of years. If the orbit is too low, the spacecraft may face orbital decay due to atmospheric friction and may have to reapply power to stay in orbit or else fall out of orbit and crash, perhaps in days or hours. Except for the possible necessity to periodically increase its orbital velocity to counteract orbital decay, a body in an astronautical orbit has no need to use propulsion to stay up.
In aviation orbit is a verb:
(as a verb) to perform a 360° circuit usually in order to delay: for safety reasons, the ATC will tell the pilot whether to orbit left or right.
Wikipedia's article on Airfield traffic pattern says:
There is also a procedure known as an "orbit", where an aircraft flies a 360° loop either clockwise or anticlockwise. This is usually to allow greater separation with other traffic ahead in the pattern. This can be the result of a controller's instruction. If at the pilot's initiative, the pilot will report e.g. "(tail number or flight number) making one left-hand orbit, will advise complete".
So in aviation, making one or more orbits is a maneuver that an airplane can make. And an airplane while flying in an orbit, like whenever it is flying, needs to be powered at all times. If an airplane in flight looses power, it will begin to fall; if power is not restored in time, the airplane will touch the ground, in either a controlled glide to an emergency landing or an uncontrolled crash landing.
Since some of the creators of TOS had aviation backgrounds, they may have imagined that many TOS orbits were not astronomical or astronautical orbits around celestial bodies, but were aviation orbits where the starship was held up by constant application of power. So there were a number of TOS episodes where the Enterprise lost power due to enemy interference and began to fall from orbit with only hours to go before destruction.
Similarly, the special effects scenes of the Enterprise in orbit around a planet showed it turning in a curved path. So far so good. Since a class M planet like the ones visited by the Enterprise would be several thousand kilometers or miles in diameter, and the Enterprise was shown hundreds or thousands of kilometers or miles above the planet's surface, the starship should have been shown making a circular path thousands of kilometers or miles in diameter. But instead the Enterprise was always shown turning in a tight curve with a diameter of only a few time the ship's length and thus only a few kilometers or miles!
So by accident or design, the special effects showed the Enterprise "orbiting" or circling around a point in space above the planet, and not "orbiting" or circling around the planet itself.
So one might speculate that possibly in those cases Enterprise was not orbiting around the planet in an astronautical orbit formed by initial velocity and gravity, but was hovering in space - held up by constant application of engine power - above a point on the surface of the planet, perhaps to have line of sight for communications and transporters if there was a landing party at that point on the surface of the planet. And for some reason Enterprise didn't stay still at that point but orbited or circled around that point in space above the planet in a path or orbit with a diameter of just a few kilometers or miles.
And you may note that Enterprise usually didn't have its bottom pointed at the planet but usually had its side pointed at the planet.
The reason for all this odd behavior may have been some arcane function of the transporter system.
At other times, the Enterprise may have put itself into normal astronautical orbits around various planets, and the decisions about what type of orbit or "orbit" to use would no doubt be based on various technical factors.
As far as I remember, in other Star trek productions starships were never in danger of falling out of orbit if they lost power. That may be because those starships always used astronautical orbits around planets, or because they never encountered enemies who sucked power out of their engines while they were using powered aviation type obits above planets. For what it is worth, the "orbital" special effects in those other Star trek productions often looked similar to those in TOS.
So it is possible that a star ship can assume a normal astronautical type of orbit around a planet, or take up a totally different powered aviation type "orbit" around a point above the surface of the planet.
I am not certain whether a "standard orbit" refers to an astronautical type of orbit or an aviation type of orbit, let alone any of the more precise details of a "standard orbit".