Anyone who has observed a number of comets, as I have over the last 54 years, knows that they come in an amazing variety of shapes and sizes. Aside from differences in mass and orbit, each one has a history: how many times has it visited the inner Solar System, and how close to the Sun has it passed?
Each time a comet passes close to the Sun it loses material: that's where its tail comes from. Some comets, like Halley, seem to have abundant reserves of material, so put on a great show most of the time. 1986 was an aberration due to a poor placement of Halley's orbit relative to the Earth's position. Other comets are quite small, like Elenin, and it takes only a coronal mass ejection to "blow them out," as happened on August 19.
Not all comet produce tails. The usual measure of a comet is that it forms a coma (expanding tenuous dust atmosphere), and Comet Elenin certainly did this. Its coma reached 200,000 km in diameter. It also shows a small tail in images made of it just prior to its encounter with the CME. No asteroid behaves like this.
I'm a bit baffled by your statement "By naked-eye observation, it doesn't look like the other famous comets" since Elenin, at its very brightest, only reached 10th magnitude, well below naked eye visibility.
In short, Elenin was an ordinary small comet, similar to many which visit the inner Solar System every year. Don't compare it to the great comets which we see only once or twice in a lifetime.