We have investigated the photophysical properties of chemically and gate-doped semiconducting single-wall carbon nanotubes (s-SWNTs). The first subband exciton oscillator strengths as obtained from a global analysis of absorption spectra are used for assessment of carrier densities and provide evidence for band-gap renormalisation (BGR) in (6,5) SWNTs. We predict that BGR of one-dimensional gate doped semiconductors is accompanied by a stepwise increase of the carrier density by Δn=32m_eff b/(πℏ)²once the electrochemical potential reaches the valence or conduction band offset with b = (0.15 ± 0.05) eV nm (m_eff - effective carrier mass). Moreover, we show that the width of the spectroelectrochemical window of the first subband exciton of (1.55±0.05) eV corresponds to the fundamental band gap of the undoped (6,5) SWNTs in our samples and not to the renormalized band gap of the doped system. We also compare spectral changes in gate doped with those of chemically doped SWNTs. Femtosecond time-resolved pump-probe spectroscopy of chemically doped SWNTs provides evidence of exciton-trion coupling. These observations as well as a previously unidentified absorption band emerging at high doping levels in the Pauli-blocked region of the single-particle Hartree band structure, provide clear evidence for strong electronic correlations in the optical spectra of SWNTs.