granulocytes are a type of leukocytes that have granules (hence the name) visible by microscopy
Yep, that's it; like you said, that's where they get the name: their appearance. Not their function or progenitor, just their appearance, and they were named long before the other factors were understood. That history goes back to at least the mid 1800s:
Paul Ehrlich's techniques, published between 1879 and 1880, for staining blood films using coal tar dyes, and his method of differential blood cell counting, ended years of speculation regarding the classification of white cells.
In 1846, Thomas Wharton Jones (1808-1891) described "granule blood-cells" in several species including humans. The term "granule cell" had also been used by Julius Vogel (1814-1880), who had previously observed similar cells in inflammatory exudates. Vogel, in turn, was aware of the work of Gottlieb Gluge (1812-1898), who had observed "compound inflammatory globules" in pus and serum that resembled eosinophils. Almost 20 years before Ehrlich developed his staining methods, Max Johann Schultze (1825-1874) performed functional experiments on fine and coarse granular cells using a warm stage microscopic technique and showed they had amoeboid movement and phagocytic abilities. Despite these earlier observations, it was Ehrlich's use of stains that heralded the modern era of studies of leukocyte biology and pathology.
Progenitor cells are cells that haven't yet matured into functional fully differentiated cells; usually the name "progenitor cell" is reserved for cell populations that are nearly differentiated and won't result in more than a couple/few final cell types. So, no, a "XYZ progenitor cell" is not the same as an "XYZ cell".
It seems like there is not a settled terminology for various classifications of immune cell progenitor cells, with different publications using different terms. For example, a figure on Wikipedia uses "myeloblasts" to describe cells that undergo either granulopoiesis to become some granulocyte, or they become monocytes:
They don't really name any general granulocyte progenitor, instead showing them all splitting off together. Others refer to "myeloid progenitors", "granulocyte/monocyte progenitor"/"GMPs", "granulocyte/macrophage progenitor" (as monocytes become either dendritic cells or macrophages), and others.
I don't see any source where a "granulocyte progenitor cell" becomes a monocyte, only that a "granulocyte/monocyte progenitor cell" does; the "granulocyte/monocyte" label seems most clearly interpreted as "granulocyte and monocyte" progenitors, so I see nothing conflicting with these cells giving rise to both granulocytes and monocytes. I also do not see evidence that there is a stage of differentiation in which a particular cell will possibly become a monocyte or neutrophil, yet will not become eosinophil nor basophil; every textbook-style reference I find shares the pattern from the Wikipedia image above or discusses a stage of differentiation in which a cell is either fated to become a monocyte or any of the granulocytes. Given the complexity of differentiation, it's certainly possible some paper has made that claim, but I see no evidence for it.