Radio frequency (RF) driven inductively coupled plasma (ICP) discharges are extensively used in a variety of industrial and technological applications due to their multiple advantages like low sheath voltages, high plasma densities, low contamination from reactor sputtering, and easily controllable ion energies. In comparison to the conventional ICPs, the Magnetic Pole Enhanced-Inductively Coupled Plasma (MaPE-ICP) scheme is a relatively new concept that offers additional attractive features such as lower electron temperature, higher plasma density, better spatial uniformity and larger area coverage capability. Therefore, the MaPE-ICP source is chosen in the present study to investigate the plasma parameters of interest in relevance to their applications. In analogy to the conventional ICPs, the MaPE-ICP also operates in two distinct modes, namely electrostatic or E-mode and electromagnetic or H-mode. These two modes exhibit significant differences in their electrical and plasma properties, and thus have motivated many researchers to study the two modes of conventional ICPs over the last two decades. However, very little work has been done in the two modes of the MaPE-ICP discharges. Therefore, the key plasma parameters and active species concentration are investigated here in the two distinct modes of the MaPE-ICP to understand the related phenomena in this modified version of ICP. In the first step, a comparative study of the electron temperature determined by Langmuir probe and the excitation temperature estimated by Optical Emission Spectroscopy (OES) is carried out in the two distinct modes of the MaPE-ICP using argon as operating gas for different applied RF powers (5-50 W) with the varying gas pressures (15-60 mTorr). The non-intrusive OES based measurements of plasma parameters like the electron temperature is very proficient for plasma processing where the application of Langmuir probe measurements has several limitations. In this study, an effort is made to find a relationship between the measured values of the electron and excitation temperatures. It is observed that the electron temperature can be easily determined from the excitation temperature in the H-mode but difficult to do so in the E-mode of the MaPE-ICP. The gases used in processing of materials and other applications are mostly electronegative in nature. Oxygen is a simple electronegative gas which is also used in various applications such as photo-resist ashing, oxidation, sterilization, and surface activation and modification. Therefore, in the second step, the study is extended to determine plasma parameters and active species concentration in the two distinct modes of the MaPE-ICP operated in oxygen for different applied RF powers (40-300 W) and gas pressures (15-60 mTorr). The key plasma parameters like electron density, electron temperature, electron energy probability function, positive and negative ions densities are determined by using Langmuir probe. Moreover, the atomic oxygen density and dissociation fraction are estimated with the help of OES. The measured parameters are compared with the reported parameters in the conventional ICPs and some interesting similarities and differences are found between the two schemes. It is observed that the MaPE-ICP presents relatively early mode transition, lower electron temperature, and much higher dissociation fraction and atomic oxygen density. These features suggest that the MaPE-ICP will be more promising for the purpose of plasma processing applications. The work will be a useful addition to the field of related studies and also for using other gases of technological interests.