The Western horoscope compatibility chart is about the compatibility of those who are typical of their Western signs. If you were born between the 1st and the 7th of the month, you are the most typical of your sign. The further away from those days of the month your birthday is, the less typical of your sign you are.
The compatibility of two people in Western astrology has to do with how much time their birthdays are apart in a year. It does not strictly have to do with their Western signs. The signs are just an easy way to identify people.
In general, those whose birthdays are within two weeks of each other or *about* four or eight months apart are more compatible. So two people can be quite a good match in Western astrology even if they are not a good match according to the Western horoscope compatibility chart.
*about* means *from two weeks earlier to two weeks later*
Similar analysis can be made in Chinese horoscope compatibility. In general, those whose birthdays are within six months of each other or **about** four multiplied by any number of years apart are more compatible.
**about** means **from six months earlier to six months later**
Please also read Horoscope by date of conception vs. horoscope by date of birth.