A MT engine (MT = machine translation) is a system-bound model for automatically translating a language into another language in a one-way manner. The methods are either rule-based (RBMT), statistical (SMT) or neural (NMT). In order to train statistical and neural MT engines, large amounts of bilingual corpora in very good linguistic quality are required.
When we talk about MT, we usually mean the NMT. RBMT and SMT are only used in special applications.