The co-ordinate conjunction "but" is a very small, and a very common word. Small and simple as it is, it has a definite meaning: it expresses contrast: "I went, but Andries stayed."

Sentence connectors are used to combine sentences.

Image credit

They also express the relationship between ideas. To show the contrast between two ideas, the following sentence connectors can be used:
But, although, despite the fact that, however, nevertheless, despite, in spite of, yet. e.g.. His rope was thin, but, it was strong. He is fat but runs fast. Although she was shy, she didn't stop with her acting.
Oddly enough, it seems to be one of the most misused words in the language, and so is its more formal twin, "however."

Image credit

Here is an example of a letter a little girl writes, "On Saturday I had a letter from Mary in which she informed me very pitifully that her little brother John died last Sunday of asthma. It is very sad indeed. Yesterday, however, the cat upset a pot of stew ..." And here is an example of the misuse of "but": "The flowers are not perennial, but they appear only in the spring." This last sentence is another example of pleonasm - do you see that logic demands that you should omit either "but" or "they"? I hope you detected more glaring examples in the list after the paragraph on pleonasm.

Nevertheless is very formal. In a less formal style, we can use conjunctions like but or yet. Nevertheless and however don't combine two clauses. They are used to emphasize the fact that the point expressed by the second clause contrasts with the first. In writing, they are separate from the rest of the sentence by a comma.
He says he is a socialist. However, he owns four houses and twelve luxury cars.

Image credit

Image credit

Sources: https://www.englishgrammar.org/sentence-connectors-showing-contra
EBH Joubert, English Grammar.

please follow me @ frieda