Among the wide variety of single fluorescent defects investigated in silicon, numerous studies have focused on color centers with a zero-phonon line around $1.28 \mu$m and identified to a common carbon-complex in silicon, namely the G center. However, inconsistent estimates regarding their quantum efficiency cast doubt on the correct identification of these individual emitters. Through a comparative analysis of their single-photon emission properties, we demonstrate that these single color centers are split in two distinct families of point defects. A first family consists of the genuine single G centers with a well-identified microscopic structure and whose photoluminescence has been investigated on ensemble measurements since the 60's. The remaining defects belong to a new color center, which we will refer to as G$^{\star}$ center, whose atomic configuration has yet to be determined. These results provide a safeguard against future defect misidentifications, which is crucial for further development of quantum technologies relying on G or G$^{\star}$ center quantum properties.