Speaking and writing are two different things.

Literal

Speaking [nominalizer-こと] [and-と] writing [nominalizer-こと] [topic-は] different-thing [copula-だ].

こと nominalizes both verbs so they can serve as nouns. と joins them as an exhaustive pair. 別物 (べつもの, 'a different thing, a separate matter') is stronger than just 違う — it implies categorically distinct entities.