"Capital G" is the constant of proportionality in Newton's law of gravit. It established a formal relationship between the masses, the distance and the resulting gravitational force. It is now assumed that G is not constant, but could depend on other, previously unknown factors.
Recognized CODATA value of 2010:
G = (6,67348 +/- 0,00080) 10 - 11 m³ kg-1 s-2. The accuracy of this value is only 0.15 %, which is very inaccurate for a fundamental constant.
"Small g" refers to the acceleration with which a freely falling body increases its velocity in the Earth's gravitational field. Average value: G = 9.80665 m/s² (CODATA value of 2010).