Yes, the Sun & Moon are the true “owners” of the sky. The other five planets are stewards of their signs, similar to how the “landlord” system worked in feudal societies.
This doesn’t change anything about how you should think about the signs. It is simply the root cause of the Male/Female (Sun/Moon) nature inherent in the 12 zodiacs.
Q/A About this…
Q: I was searching for rāśī videos and found one that says Leo-Capricorn belong to the Sun, while Aquarious through Cancer belong to the Moon. He said Sun-owned signs are more external, and Moon-based are more internal.
A: If we adopt this concept, we will fall into some preposterous misunderstandings. For example: Aries and Gemini would be “introverted” and Virgo “extroverted.”
The correct understanding is that the Moon owns every even zodiac (2 – Taurus, 4 – Cancer, 6 – Virgo, 8 – Scorpio, 10 – Capricorn, 12 – Pisces), and the Sun owns every odd zodiac (1 – Aries, 3 – Gemini, 5 – Leo, 7 – Libra, 9 – Sagittarius, 11 – Aquarius). This will give you the correct conception of gender and the internal/external dynamic (which is really just an aspect of gender).
Here is a relevant video: