"both" und "and"

• both + adjective + and + adjective

  Beispiel:
  She's both attractive and intelligent.

• both + noun + and + noun

  Beispiel:
  I spoke to both the manager and his assistant yesterday.
  NOT: I both spoke to ....

• both + clause + and + clause

  Beispiel:
  He both manages the accounts and organises logistics

"but" or "however" may be used to create a contrast

Gebrauchen Sie das eine oder das andere - aber nicht zusammen.

• Vergleiche:
  The organization's (AE) service is excellent, but they are quite expensive.
  The organisation's (BE) service is excellent, they are quite expensive however.

• NOT
  The organisation's service is excellent, but however, they are quite expensive.
  Having said that you will experience native speakers making this mistake.

However (informal) / nevertheless (formal)

These words are used to emphasise the fact that the second point contrasts with the first.