The cluster of helium stars around Sgr A* has been re-observed with the BEAR spectro-imager on CFHT, in the 2.06 mu m helium line, at a spectral resolution of 52 km s(-1) and on a field of similar or equal to 40 ''. This new analysis confirms and completes a previous study at a spectral resolution of 74 km s(-1) and on a smaller field of 24 '', corresponding to the central parsec (Paumard et al. 2001). Nineteen stars are confirmed as helium stars. These observations led to a clear differentiation between two groups of hot stars based on their emission linewidth, their magnitude and their positions relative to Sgr A*. The first class of 6 members is characterized by narrow-line profiles (FWHM similar or equal to 200 km s(-1)) and by their brightness. The other, fainter in K by an average of 2 mag, has a much broader emission component of width similar or equal to 1,000 km s(-1). Several of the emission lines show a P Cygni profile. From these results, we propose that the narrow-line group is formed of stars in the LBV phase, while the broad-line group is formed of stars in or near the WR phase. The division into two groups is also shown by their spatial distribution, with the narrow-line stars in a compact central cluster (IRS 16) and the other group distributed at the periphery of the central cluster of hot stars. HST-NICMOS data in Pa alpha (1.87 mu m) of the same field reveal a similar association. The identification of the Pa alpha counterpart to the He I stars provides an additional element to characterize the two groups. Bright Pa alpha emitters are found generally associated with the narrow-line class stars while the weak Pa alpha emitters are generally associated with the broad-line stars. A few particular cases are discussed. This confirms the different status of evolution of the two groups of massive, hot stars in the central cluster. As a by-product, about 20 additional candidate emission stars are detected in the central, high-resolution 19 '' field from the NICMOS data.