The aim of this paper is to present some new observations about $w$-distance (in the sense of O. Kada, T. Suzuki, W. Takahashi, \emph{Nonconvex minimization theorems and fixed point theorems in complete metric spaces}, Math. Japonica extbf{44}, 2 (1996), 381-391) and $F$-contractions (in the sense of D. Wardowski, \emph{Fixed points of a new type of contractive mappings in complete metric spaces}, Fixed Point Theory Appl., extbf{2012}:94 (2012)). Both concepts have been examined separately a lot, but there have been few attempts to connect them. This article is a step in filling this gap. Besides, some comments and improvements of results in the existing literature are presented.