[sentence (plain form)] 。だが、[sentence]
[sentence (polite form)] 。ですが、[sentence]
Note: だが and ですが function as sentence-initial conjunctions connecting two contrasting sentences. だが is plain/literary; ですが is polite.
だが and ですが are conjunctions meaning "but," "however," or "nevertheless." They are used to connect two statements where the second contrasts with, contradicts, or is unexpected given the first.
だが carries a formal, somewhat stiff tone and is most commonly found in written language such as essays, news articles, novels, and formal speeches. It typically appears at the beginning of a new sentence to introduce a contrasting idea.
Because of its literary quality, だが sounds unnatural in casual everyday conversation. In spoken Japanese, でも or けど are far more common for expressing "but."
ですが is the polite equivalent and is used in polite speech and writing. It can appear at the beginning of a sentence or between clauses, and is common in business settings, customer service, and formal conversations.
ですが is also common as a soft conversation opener or to politely introduce a topic, similar to "well..." or "actually...":