Remote sensing of the Earth has demonstrated that photosynthesis is traceable as the vegetation red edge (VRE), which is a steep rise in the reflection spectrum of vegetation, and as solar-induced fluorescence. This study examines the detectability of biological fluorescence from two types of photosynthetic pigments, chlorophylls (Chls) and bacteriochlorophylls (BChls), on Earthlike planets with oxygen-rich/poor and anoxic atmospheres around the Sun and M dwarfs. Atmospheric absorption, such as H2O, CH4, O2, and O3, and the VRE obscure the fluorescence emissions from Chls and BChls. We find that the BChl-based fluorescence for wavelengths of 1000-1100 nm, assuming the spectrum of BChl b-bearing purple bacteria, could provide a suitable biosignature, but only in the absence of water cloud coverage or other strong absorbers near 1000 nm. The Chl fluorescence is weaker for several reasons, e.g., spectral blending with the VRE. The apparent reflectance excess is greatly increased in both the Chl and BChl cases around TRAPPIST-1, due to the fluorescence and stellar absorption lines. This could be a promising feature for detecting the fluorescence around ultracool red dwarfs using follow-up ground-based observations at high spectral resolution; however, this would require a long time around Sunlike stars, even for a LUVOIR-like space mission. Moreover, the simultaneous detection of fluorescence and the VRE is the key to identifying traces of photosynthesis, because absorption, reflectance, and fluorescence are physically connected. For further validation of the fluorescence detection, the nonlinear response of biological fluorescence as a function of light intensity could be considered.