Many interpret the “mortally wounded head” in (Rev. 13:3) and the “beast whose deadly wound was healed” (Rev. 13:12) as the same thing. But that ignores the different imagery and time frame wherein these wounds exist:
The author switches from past [Rev. 13:1-11] to present tenses in Rev. 13:12–18, though apart from producing a more vivid narrative, the reasons for this stylistic change are not immediately evident.-Aune, D. E. (1998). Revelation 6–16 (Vol. 52B, p. 757). Dallas: Word, Incorporated.
The wounds are not the same. The first was a “death blow” to the head that killed it (Rev. 13:3). The second survived a sword stroke (Rev. 13:14). Although weakened it was not killed as in the first.
The wounded head is ancient Babylon, the wounded Beast is the Revived Roman Empire that appears in the end time.
John provides the interpretive key alluding to Daniel 7:2-8, where four beasts rise, but they total seven heads. The first two beasts have one head each, the third beast has four heads, that totals 6 heads. Therefore, the head of the fourth beast is the seventh head (Dan. 7:2-7). The final form of the empire (eighth king Rev. 17:11) is the Grecian Roman Empire is the final ten-horned ten-toed form (Dan. 2:44; 7:7) containing the rebuilt city of Babylon.
Confirming Revelation’s end time Roman Empire Beast is a composite of Daniel’s last beast, the same animals leading up to it are in both. But notice the order of appearance is reversed, in Daniel its lion, bear then a leopard. In Revelation its leopard, bear then a lion. This confirms they are not the same beast. Unlike Daniel’s seven successive kingdoms rising from the sea, John’s Beast rises from the sea a single kingdom FROM them. Therefore, the ten horned version of Daniel’s fourth beast, is the seven head ten horned Beast of Revelation.
But a clue many miss is the different list of kingdoms the angel uses in Revelation 17:10. The count does not begin with Babylon (Dan. 2:38; 7:4), it begins with the Medes and Persians (Daniel 8:3, 9-12). Therefore, the wounded head (Ancient Babylon) “was and is not” (in ruins) and is healed (restored in the Grecian Roman Empire) and so “of the seven” but itself is an eighth king (Rev. 17:11).
9 “Here is the mind which has wisdom. The seven heads are seven mountains on which the woman sits,
10 and they are seven kings; five have fallen, one is, the other has not yet come; and when he comes, he must remain a little while.
11 “And the beast which was and is not, is himself also an eighth, and is one of the seven, and he goes to destruction. (Rev. 17:9-11 NAS)
There are seven kings, five have fallen:
1) Medes Persians;
2-4) Grecian = 2) (Seleucus) Syria; 3) (Ptolemy) Egypt; 4) (Cassander) Macedonia;
5) Lysimachus) Asia Minor.
6) One is” Rome;
7) Britain whose mandate over Palestine was only a short while. The Balfour Declaration supported the establishment of Israel but Britain’s mandate over Palestine was short lived. This is consistent with Scripture listing only nations that impacted Israel in a meaningful way. The League of Nations/United Nations isn’t a kingdom and never did anything binding. America makes her appearance with Britain as the Beast with two horns like a lamb.
8) The Eighth King is the Grecian (leopard body=Syria) form of the Revived Roman Empire that has the rebuilt ancient city of Babylon as its capital.
3 And I saw one of his heads as if it had been mortally wounded, and his deadly wound was healed. And all the world marveled and followed the beast.
4 So they worshiped the dragon who gave authority to the beast; and they worshiped the beast, saying, “Who is like the beast? Who is able to make war with him?” (Rev. 13:3-4 NKJ)
Ancient Babylon (mortally wounded head) died and was buried under the desert sand. It is “healed” in the end time when fallen angels return claiming to be extraterrestrials. The magic of fallen angel technology inspires Progressive Globalists to worship the New World Order of the Beast and its “Dragon Commander.” That is the meaning of Babylon rising from the abyss of demons (Rev. 17:8; 9:1-3). 
Wounded by the sword and lived
This Final Version of the Roman Empire and the power of Emperor Adonikam is wounded by a sword when Russia, Iran and Turkey reject the new World Order. They are the forces from Babylon’s North that destroy her (Jer. 50:41-42; 51:47-48). It then goes off into total destruction fulfilling the OT prophecies (Jer. 50:3, 13, 39-40; 51:29. Rev. 18:2-10). Although Babylon’s destruction causes global Economic Depression (Rev. 18:11), Emperor Adonikam and his beast kingdom survive the wound.
Then the formerly Christian (and liberty loving free market) nations of Britain and America unite under a “False Prophet” President or Prime Minister and ally themselves with Antichrist Beast. Against this alliance Russia, Iran and Turkey cannot war. They stand down and join the Beast’s Federation.
Therefore, the wounds are completely different. The wounded head was the ancient kingdom of Babylon restored in the ten horn Grecian Roman Empire that rises in the end time. The wounded Beast is that Empire Beast when its rebuilt capital city of Babylon is destroyed by the sword by forces from her North. It survives and regains control with the aid of the two horned beast like a lamb Britain and America. Now speaking like a Dragon, they support the Antichrist, totalitarianism and controlled markets.
For more on this click:
Revelation 13 Seven Heads and Ten Horns Explained
Adonikam the “man of sin” false Christ who morphs into the Beast Son of Destruction after 3 ½ years (2 Thess. 2:3-4) also ascends from the abyss (Rev. 11:7) because he is the literal seed of Satan, a hybrid angel human creation.
The Nephilim will return disguised as Extraterrestrials with Satan as their Dragon Commander (Rev. 12:7-9). The “ancient alien theory” is the satanically energized strong delusion (2Th. 2:11-12; Rev. 16:13-14) The “flying frog” demons out of their mouths “the BIG LIE” Satan and his angels are extraterrestrials. They will cause the Great Revolt (2Th. 2:3-4) against even the definition of God, opposing it while exalting the hybrid 666 Beast as above “the Elohim extraterrestrial gods” hoping to change times and law of civil society (2Th. 2:4. Dan. 7:8, 25; 8:10-11, 24; 11:36-39). The hybrid Satan-human is “Satan’s seed” (Gen. 3:15) “The Beast”(Rev. 16:13) “the Antichrist” (1Jn. 2:18; 22-23; 4:3. 2Jn. 1:7) whose human name will be “Adonikam” (Rev. 13:18; Ezr. 2:13). On this see: The 666 Riddle solved
Satan craftily spoke through a serpent corrupting Eve from the simplicity of God’s truth beguiling her to eat (2Cor. 11:3) from the tree of knowledge (Gen. 3:1-6). Satan is called a cedar tree (Ezek. 31:8-11), whom the fallen angels followed (Ezek. 31:6). Christ “the ruler of the nations” and His angels will cast them into “the pit” (Ezek. 31:11-14). In Ezekiel 31:3 this “cedar” is called Assyria, his “seed” then would be “the Assyrian” (Mic. 5:5-6; Isa. 14:25-27), the apostate Jewish Christian named Adonikam (King of the North) Satan’s seed (Gen. 3:15).