"Speak English". It's to emphasize someone's language ability. I would say that it has hidden (can).
You speak a language. You speak English. I speak French. He speaks Spanish. She speaks Italian. What languages do (or can) they speak?
"in English (or any language)" is an adverbial aspect, to provide more detailed description.
For example, consider a sentence "He spoke to me", is a general statement, without stating where, how, when, or what content.
He spoke to me yesterday.
He spoke to me loudly and quickly.
He spoke to me in his room.
He spoke to me IN ENGLISH.
He spoke to me about his mother.
"IN English" is an adverbial aspect.
Combining all these, you get a long descriptive sentence.
He spoke to me yesterday in his room about his mother, in English, loudly and quickly.
You can change "speak" to "say" as in "say in English", but you can't say "He says English". You have to say "He says in English".