The most common allotrope of tungsten, {\alpha}-W, has a superconducting transition at a temperature of ~11 mK. However, two other forms of tungsten have been reported to have superconducting transitions in the temperature range Tc ~ 2-5 K when synthesized as thin films: Crystalline \b{eta}-W and amorphous W (a-W). In this work we carry out a systematic study of W films synthesized using d.c. magnetron sputtering, using transport, low frequency magnetic shielding response, and transmission electron microscopy. Our results show that while a-W is indeed a bulk superconductor, superconductivity in \b{eta}-W probably originates from an amorphous phase that forms along with the \b{eta}-W phase. Our findings reconcile some of the anomalies earlier reported in \b{eta}-W, such the very small superconducting gap and the decrease of Tc with increase in film thickness.
