and vs both

Used simply to connect two noun phrases, adjectives or adverbs. 

Introducing a parenthetical or explanatory clause. 

If; provided that. 

Used to connect more than two elements together in a chain, sometimes to stress the number of elements. 

connecting two well-formed formulas to create a well formed formula that requires the new formula to only be true when each of the two are true. 

Used to connect certain numbers: connecting units when they precede tens (not dated); connecting tens and units to hundreds, thousands etc. (now often omitted in US); to connect fractions to wholes. 

Simply connecting two clauses or sentences. 

Connecting two identical elements, with implications of continued or infinite repetition. 

Introducing a qualitative difference between things having the same name; "as well as other". 

Used to combine numbers in addition; plus (with singular or plural verb). 

Introducing a clause or sentence which follows on in time or consequence from the first. 

Introducing the continuation of narration from a previous understood point; also used alone as a question: ‘and so what?’. 

Used to connect two verbs where the second is dependent on the first: ‘to’. Used especially after come, go and try. 

To breathe; whisper; devise; imagine. 

Including both of (used with and). 

Each of the two; one and the other; referring to two individuals or items.