A drift-kinetic and a gyrokinetic model able to describe the plasma dynamics in the tokamak periphery are presented, which take into account electromagnetic fluctuations at all relevant scales, allowing for comparable amplitudes of background and fluctuating components. In addition, the models implement a full Coulomb collision operator, and are therefore valid at arbitrary collisionality regimes. For an efficient numerical implementation of the models, the resulting kinetic equations are projected onto a Hermite-Laguerre velocity-space polynomial basis, obtaining a moment-hierarchy. The treatment of arbitrary collisionalities is performed by expressing the full Coulomb collision operator in guiding-center and gyrocentre coordinates, and by providing a closed formula for its gyroaverage in terms of the moments of the plasma distribution function, therefore filling a long standing gap in the literature. The use of systematic closures to truncate the moment-hierarchy equation, such as the semi-collisional closure, allows for the straightforward adjustment of the kinetic physics content of the model. The first numerical studies based on our models are carried out, shedding light on the interplay between collisional, using the Coulomb collision operator, and collisionless mechanisms.