The translation process in statistical machine translation (SMT) is shaped by technical constraints and engineering considerations. SMT explicitly models translation as search for a target-language equivalent of the input text. This perspective on translation had wide currency in mid-20th century translation studies, but has since been superseded by approaches arguing for a more complex relation between source and target text. In this paper, we show how traditional assumptions of translational equivalence are embodied in SMT through the concepts of word alignment and domain and discuss some limitations arising from the word-level/corpus-level dichotomy inherent in these concepts.