Exactly? Oh, well… The Sun is not 'you' so much as all the planets in the horoscope chart are 'you'. But the Sun is a part of that.
"The Sun" represents 'you' taking in the world around you, a world with which you must interact every moment of your life. By interaction with 'it' (the world) you bring perceptions (Moon) into the mind where they reside as ideas (Mercury) in memory; these ideas will influence and shape (Venus) who this 'you' ultimately is, and will be acted (Mars) upon, if not immediately and deliberately then at some future time, when they will be drawn upon to 'change the world' (Jupiter) to suit us and others, to the best of our 'limited abilities' (Saturn).
We are all (in)formed by our ideas. The Sun symbolizes the "we" who is being formed this way.
We are each the subject of the world around us. Being a subject creates a world (of stored ideas of things); and having a world creates a subject. (Duality)
A "sign" is an indication that something is. It comes upon us by observation and interpretation of events --like if a friend is suddenly quiet, we may take it as a sign that there is something wrong. A "take" is like a snapshot of circumstances, often with a specific meaning that stands out for that moment in time. A "take" is not done with deliberation but spontaneity; therefore, a "take" always represents something "true to me."
You have a way of taking in the world around you that is true to you --true to who you are. Your natal chart is also a take --a divinatory take on 'you' at a particular time in your life. And there is a third take involved that brings it all together as "astrology" --one that the astrologer makes in looking at the symbols on the chart. He makes a take on 'you'.
The astrological Sign of the Sun in a chart is an indicator of the subject's take on the world. The constellation "Leo" in the heavens represents a stage in the development of "Man" where he takes his place on a seat of power... like his name-sake, the king of the beasts. He has power through knowledge of who 'he' is ("I am."), power to control his world, and power that attracts others to him "like moths to the flame." All the personality traits that can be associated with such things are at Leo's command.
Think Simba "taking his place" on Pride Rock --life returns when the "king" is (in)formed in 'you'. ("He lives in you.")
To say that "the Sun is in (a Sign)" is to say that the Sign is the nature of the "take" that an astrologer, who looks at the horoscope chart, makes in consideration of any evaluation of your take on the world. Astrology happens when the astrologer looks at the symbols and makes a connection between its take on 'you' that happens for us at a single moment in time and (for the Sun) your take on the world that happens every moment of your life.
The Sign that is Rising on the Eastern horizon at the time of birth is part of a second divinatory method within the horoscope chart utilizing astrology's Houses (as opposed to planets). It also represents 'you' but the significant difference is that the Houses symbolize things and events in our lives, so in the astrologer's take of the First House (which the Rising Sign borders) he interprets things and events that take place in relation to you.
"Relation" is the key word --all the Houses are about relating to 'you' (the subject). In taking in the world around you and becoming subject to it, a relation is born between 'you' and 'it'. Well, that means that necessarily all those it's that make up the world out there also have a relation to you. The Rising Sign defines the First House, wherein things and events relate to you.
The Rising Sign is often said to express "how others see you," because they are in relation to you. They see you from out there, and can reveal things that you might not have known about yourself (like that zit on the end of my nose!
). The Rising Sign gives us another's take on you --things like your physical appearance, and (as Isarma said) the "face" that the world sees in things you say and do.
Scorpio in the heavens represents a stage of "Man" where he is part of a duo, a couple, but still very much himself. He hasn't yet "given in the dark side" (relatively speaking) and become fully a partner in a partnership, so he finds his indulgences come at the expense of the partnership, a situation that is inherently unfair. The Sign of Scorpio pulls such personality traits out his pocket, often when people least expect it.
Hope this helps.
(They sometimes confuse me too.)