Since both types of tails point generally anti-sunward, and a comet's orbit may be oriented at almost any angle to the earth's orbit, whether a long tail is visible from earth is a matter of chance. So indeed, the different appearances of various comets, or even the same comet, can be deceiving. Once Halley and Newton figured out how the orbits of comets could be described, the next interesting question was why any comet has the orbit it has. As you saw in the Origins section, the formation of the Oort Cloud around the inner solar system put many comets into orbits where they no longer encounter large objects like Jupiter at close range, and are are much farther from the sun than Pluto, even at perihelion. Oort suggested that the gravity of passing stars might exert a gravitational pull on some comets, making their orbits longer and narrower.
Stars pass each other within galaxies, although they also orbit around the galactic center.
Another star passing by the Sun would be a relatively common event in the course of 4.5 billion years. When the star passes, the new orbit remains. The more stretched-out an ellipse becomes, the closer the focus points are to the ends. This means the longer and flatter a comet's orbit becomes, the closer it is to the sun at its perihelion. If the orbit becomes narrow enough, the comet passes close enough to the sun, and becomes bright enough, to be observed with a telescope, binoculars, or the naked eye.