Speech is production of the sounds that make up spoken language. Language is understanding and expression through the organised system of symbols and words to communicate meaning.
Speech is produced using the lips, jaw, tongue, throat and larynx (voice box). Language can be written, read, gestured, signed, spoken, listened to, and expressed through body language.
When we talk about 'language' in general we do not mean English, French, Chinese, but instead the overall system that underpins any and all specific languages, including sign languages. Some people have difficulty with their speech or language abilities however it is possible to have problems with both.