I will try to explain my view of the Beast of the Sea (13:1) and that it is identical to the Beast of the Abyss.
For the sake of simplicity, I will not, at the outset, quote classical NT-lexics like Bauer or Kittel, because I assume that everyone can verify this for himself. I'll just present my view:
The sea of which he writes (13:1) is, in the usual allegorical sense understood across the churches (which I also hold in this case), identified with the wicked according to Isa 57:20. The "sea," then, expresses both the "mass" of humanity, and the constant restlessness and "spilling over" of opinions in rapid succession from one place to another. The "sea" represents a certain contrast to the (unfaithful!!!) "earth". If the "sea" of people can be understood as meaning that they do not express any fixed position (see the book by the Polish sociologist Zygmunt Bauman: Liquid Modernity), the people who represent the "earth" may have had some contact with something solid, some "rock that is Christ", but sooner or later they abandoned it or even betrayed it. Out of them will come a false prophet.
Back to the "sea". How is this related to the abyss? An explanation of how to understand the function(!!!) of "abyssos" is provided by Rev. 20:1 and 20:7. In (20,1) it is stated that the angel has the keys to the abyss and Satan is cast into it. In 20,7 it is written that he is released from "prison" after a period of 1000 years. Abyssos thus has the function of a "prison", some controlled place where one either enters or is released from. This is illustrated in Luke 8:31 where the demons plead with Jesus not to be put into the abyss.
Where is abyssos located? If we accept the eschatological meaning of the word abyssos, as "prison," then an interesting answer is offered in (18:2), where it is written that Babylon the Great is the place of the "prison" of all unclean spirits. This is a very strong suggestion to consider the identity of Babylon the Great... (but that is a separate topic). The idea that there is a prison for spirits is also hinted at in 1 Peter 3:19.
If I focus on Revelation, there is always something that comes out of the abyss that is identified as a woe (9:12): it is the apocalyptic locusts of 9:1 (cf. 9:11) or just the Beast of the abyss (17:8).
What is the connection with the sea? If I accept that "a-byssos" means the bottomless depths of some waters, and there is a demonstrable connection between the waters of the sea (Gen 1:2 or Ps 105:9 (106:9) according to the LXX "The sea of reeds dried up...you led them in the abyss, as in the wilderness...") then the statement in 11:7 (17:8) that the Beast will come up in the bottomless depths of the human "sea" is just a refinement of where he will come up from.
The place of origin of the Beast of 13:1 and 17:8 is identical.
However, this does not necessarily prove that they are also one and the same Beast. Their number must be somehow differently defined.
For me, the defining number for the Beasts is the numerals: if in 13:11 it is stated that the false prophet (an animal from "the earth") is identified as "another" and immediately afterwards, in 13:12, that he takes over the power of the "first" animal, then only two animals are defined here. The image of the Beast is also only one (though it is assumed that it will be multiplied, but it will be the same as the image of Caesar on the coins), and the Beast will have a name (13:17-18). In 14:9, as well as 14:11; 15:2; 16:2; 16:10 (the throne of the Beast!) to 16:13, the Beast is mentioned with an image in the uniform usu. In 16:13 the Dragon, the Beast and the prophet are mentioned again, and from these come 3 unclean sayings. Again the number of actors is defined.
The final proof for the unity of the Beast from 13:1 and 17:8 is provided by 19:20: here the Beast and the false prophet are named, and those who received the χαραγμα and worshipped the image (according to chapter 13). Subsequently, the Beast and the false prophet are cast into the lake of fire. It is not stated that the two Beasts and the false prophet are cast into the lake of fire.