Those words were written by Daniel. As the New Living Translation Study Bible says regarding author and date,
“Scholars have endlessly debated the date at which the book of Daniel
was put into its final form. Most conservative scholars argue that
Daniel wrote the book in the late 500s BC… and the author places
Daniel in the 500s (2:1; 5:1;10:1).”
This means that Daniel had no awareness of how Jesus Christ, hundreds of years later, would show his connection with the prophetic matters he wrote about. As you ask what Daniel believed, it seems sensible to confine answers to the words of Daniel, and how he would view matters as a Jewish exile in Babylon. His three Jewish friends were close to him and their experiences would also be significant as to understanding the amazing events they witnessed.
This means that what Daniel wrote in chapter 3 about the three young men being thrown into the blazing furnace for not bowing to Nebuchadnezzar’s image relates to what he wrote many years later in chapter 10. Daniel recorded the king’s words of astonishment,
“Lo, I am seeing four men loose, walking in the midst of the fire, and
they have no hurt; and the appearance of the fourth [is] like to a son
of the gods… Blessed [is] the God of Shadrach, Meshach, and Abed-Nego,
who hath sent his messenger [angel in other translations], and hath
delivered his servants who trusted on him.” (vss. 25 & 28 Young’s
Daniel knew that three men were thrown into the furnace, four were seen walking in it unharmed, and three came out. Although Daniel did not say the fourth man only appeared to be a man, he recorded the king as describing the fourth man as appearing to be more than a merely mortal man.
Daniel also knew that God gave him understanding of dreams and also gave him visions. He writes in chapter 9 of the vision given to him, and of “the man, Gabriel, whom I had seen in the vision at the beginning, being caused to fly swiftly,” Gabriel saying he had been sent to grant Daniel understanding of the matter in the vision. In chapter 10 another vision is given to Daniel but the men with Daniel did not see the vision – only he did – that of a man of incredible appearance. Daniel uses the Hebrew plural of 'enosh for the men in verse 7, but the Hebrew 'ish for the man in verse 5. And words for divine and angelic appearances in his book occur often. According to The Companion Bible notes they are in 3:25; 4:13, 17, 23; 6:22; 7:16; 8:13, 14, 16-26; 9:21; 10:4-8, 10, 16, 18, 20; & 12:1, 5, 6. Appendix 14 on this is worth quoting:
“There are four principal Hebrew words rendered ‘man’, and these must
be carefully discriminated… They represent him from four different
points of view.
- ’Adam, denotes his origin, as being made from the dust of the Adamah ground (Lat. Homo).
- ’Ish, has regard to sex, a male (Lat. Vir).
- ’Enosh, has regard to his infirmities, as physically mortal, and as to character, incurable.
- Geber, has respect to his strength, a mighty man.
[Re. ’Ish] … A great man in contrast with ordinary men
(Ps. 49:2, where ‘low’ are called the children of Adam, and the ‘high’ = children of ’Ish. So Ps. 62:9 and Isa. 2:9 &c). When God is spoken of as a man, it is ’ish
(Ex. 15:3. So Josh. 5:13, Dan. 9:21; 10:5; 12:6,7; Zech. 1:8 &c).
[Re.’Enosh] First occurrence Gen. 6:4, men of name. Always in a bad
sense… Dan. 4:16”.
Note how Daniel chose different Hebrew words in 10:5 & 7? He was distinguishing the glorious appearing of that man in verse 5 from the ordinary men in verse 7. Now, what light does that throw on 10:16 & 18, as you specifically ask about?
In verses 16 and 18 Daniel uses the word ’Adam in the phrase, ‘like the similitude of the sons of men’ [TCB]. But he avoids saying this was, merely, an actual son of Adam, as are all men. No. He is careful to set this one apart by detailing the glorious features which no mortal man can boast of having, hence saying this one only appeared to be like a man. Context shows Daniel knew he had come from God with a message of authority, in answer to his earlier prayer and fasting. No mere human would have known anything that that messenger knew! Daniel’s choice of words show that, and the whole of his written record shows that he believed in the existence of heavenly messengers who but appeared in some outward respects to be human, but who had additional features that were supernatural.