The definition of end-to-end software and out-of-the-box software may be the following:
End-to-end software solution - is a software, which is all supplied by its provider, without assistance from a third-party. It is a solution supplied from end to end (from provider to customer).
Out-of-the-box software solution - is a software that works immediately after install. It doesn't require any modifications, modules or other third-party tools. Out-of-the-box software works "after it is taken out of the box".