Although we know that the Axe carried by Lord Parashurama was provided to him by Lord Shiva, it is not mentioned clearly whether it is Pashupatastra which has similar features. is it the same as Pashupatastra?
No, Lord Parashuramas axe is not Pashupatastra. As described in this chapter of Anushashana Parva, Upamanyu describes Pashupatastra and axe separately which were present in the hands of Mahadeva:
That bow is celebrated under the name of the Pinaka and is in reality a mighty snake. Indeed, that snake of seven heads and vast body, of sharp fangs and virulent poison, of large neck and the masculine sex, was twined round with the cord that served as its bowstring. And there was a shaft whose splendour looked like that of the sun or of the fire that appears at the end of the Yuga. Verily, that shaft was the excellent Pasupata' that mighty and terrible weapon, which is without a second, indescribable for its power, and capable of striking every creature with fear. Of vast proportions, it seemed to constantly vomit sparks of fire. Possessed of one foot, of large teeth, and a thousand heads and thousand Stomachs, it has a thousand arms, a thousand tongues, and a thousand eyes. Indeed, it seemed to continually vomit fire. O thou of mighty arms, that weapon is superior to the Brahma, the Narayana, the Aindra, the Agneya, and the Varuna weapons. Verily, it is capable of neutralising every other weapon in the universe. It was with that weapon that the illustrious Mahadeva had in days of yore, burnt and consumed in a moment the triple city of the Asuras. With the greatest ease, O Govinda, Mahadeva, using that single arrow, achieved that feat. That weapon, shot by Mahadeva's arms, can, without doubt consume in half the time taken up by a twinkling of the eyes the entire universe with all its mobile and immobile creatures. In the universe there is no being including even Brahma and Vishnu and the deities, that are incapable of being slain by that weapon. O sire, I saw that excellent, wonderful and incomparable weapon in the hand of Mahadeva. There is another mysterious and very powerful weapon which is equal or perhaps, superior to the Pasupata weapon. I beheld that also. It is celebrated in all the worlds as the Sum of the Sula-armed Mahadeva. Hurled by the illustrious deity, that weapon is competent to rive the entire Earth or dry up the waters of the ocean or annihilate the entire universe. In days of yore, Yuvanaswa's son, king Mandhatri, that conqueror of the three worlds, possessed of imperial sway and endued with abundant energy, was, with all his troops, destroyed by means of that weapon. Endued with great might and great energy and resembling Sakra himself in prowess, the king, O Govinda, was slain by the Rakshasa Lavana with the aid of this Sula which he had got from Siva. The Sula has a very keen point. Exceedingly terrible, it is capable of causing everybody's hair stand on its end. I saw it in the hand of Mahadeva, as if roaring with rage, having contracted its forehead into three wrinkles. It resembled, O Krishna, a smokeless fire or the sun that rises at the end of the Yuga. The handle of that Sula, was made of a mighty snake. It is really indescribable. It looked like the universal Destroyer himself armed with his noose. I saw this weapon, O Govinda, in the hand of Mahadeva. I beheld also another weapon, viz., that sharp-edged battle-axe which, in days of yore, was given unto Rama by the gratified Mahadeva for enabling him to exterminate the Kshatriyas. It was with this weapon that Rama (of Bhrigu's race) slew in dreadful battle the great Karttaviryya who was the ruler of all the world. It was with that weapon that Jamadagni's son, O Govinda, was able to exterminate the Kshatriyas for one and twenty times. Of blazing edge and exceedingly terrible, that axe was hanging on the shoulder, adorned with a snake, of Mahadeva. Indeed, it shone on Mahadeva's person like the flame of a blazing fire. I beheld innumerable other celestial weapons with Mahadeva of great intelligence.
So, it is clear from the above passage that Lord Parashurams axe is different from Pashupatastra. I discuss in my answer here how Lord Parashurama received axe from Lord Shiva.