A series of posts (one dating back to 2004) by Andrew Gelman (Columbia--Statistics), including links to helpful papers, provides a nice overview of the array of potential errors flowing from under-powered papers. A refresher on the nomenclature (here) sets forth the basics.
"A Type 1 error is commtted if we reject the null hypothesis when it is true. A Type 2 error is committed if we accept the null hypothesis when it is false. A Type S error is an error of sign. A Type M error is an error of magnitude."
Later posts (here), along with relevant papers (here and here), develop the issue further. Insofar as the number of papers I see that neglect reporting results from basic power tests remains far too large, these links might interest some readers.