In the past decade, significant progress has been made towards the lattice QCD calculation of parton distribution functions (PDFs). The most widely used approach for such calculation is large-momentum effective theory (LaMET), which starts from a quasi-PDF defined from the matrix elements of equal-time Wilson-line operators, and then expand and match it to the PDF at large momentum. The quasi-PDF method has undergone profound development and reached the stage of precision calculation with controlled power corrections. Recently, a new idea within the LaMET framework was proposed to calculate the PDF from quark and gluon correlators in the Coulomb gauge. The distinctive feature of this method lies in its absence of Wilson lines and the accompanying linear power divergences, which not only offers computational advantages but also significantly simplifies the process of lattice renormalization. In this talk, I will show how these Coulomb-gauge correlators can be used to calculate PDFs and all the other parton distributions, and demonstrate its equivalence to the gauge-invariant quasi-PDF method with a lattice calculation of the pion valence quark PDF.