Contradiction (But / However)

Writing an essay, a news article, or giving a formal presentation.

A。しかし、～B。 vs ～けど、～　/　A。でも、～B。: Use しかし. けど and でも are the everyday spoken 'but' and read as too casual in writing. しかし is the neutral written contrast; だが is a blunter written alternative, and けれども is more formal still.

The second statement holds true even though the first would lead you to expect otherwise.

A。それでも B。 vs A。でも、～B。: Use それでも ('even so', 'nevertheless') when you concede the first point and assert the second anyway. Plain でも only marks a contrast; それでも adds that the result defies what the first clause implies.

Stating a rule or an offer, then attaching the condition it comes with.

A。ただしB。 vs A。ただB。: Use ただし. It introduces a binding exception to what was just stated, which is why it runs through contracts, notices and terms. ただ softens with a passing reservation ('though, mind you') and is too loose to carry a condition anyone has to obey.

You want to take some of the force out of a claim you have just made yourself.

A。もっとも B。 vs A。ただB。: Use もっとも. It concedes a qualification to your own statement ('though, to be fair...'), so the sentence reads as a considered position. ただ just adds a separate reservation and does not carry that self-correcting tone.