Contrary to the horoscope that is based on your star sign, the birth horoscope is a much more personalized forecast, which takes your date and time of birth into account. The birth horoscope is also known as natal horoscope or birthday horoscope and even birth chart. It identifies the way in which the planetary movement and the transits through the skies affect you based on the positions of those planets in your astrology chart.
Your birthday horoscope is being affected by the transits of “fast” planets, such as the Moon (which changes nearly every day), Mercury and Venus, but also by planets who take their time in their journey through the Solar System, such as Pluto and Uranus. Depending on the aspects those transiting planets form with the positions those planets occupy in your astrology chart, some of those influences will be noticed instantly, while others will be felt in a longer term. Your birth horoscope will not be much different on a daily basis, since most of the planets (apart from the Sun and Moon) need at least 3 weeks to transit through the signs, however, the movement of the Sun gives a pretty accurate idea about how the Sun horoscope is shaped just a bit differently every day.
In order for you to have an accurate horoscope reading, it would be good to read the daily horoscope for your star sign, the daily horoscope of your Ascendant Sign (Or Rising Star) and also your birthday horoscope. That way, you will have great insight into both how the Sun movement affects you in a first level (i.e. daily horoscope of your Sun sign and your Ascendant) and how the rest of the planets currently interact with your natal astrology chart.