Is the first version without quotation marks the American way of punctuation?

The author of Touched, Jane Straus, wrote in the first chapter:

Georgia went back to her bed and stared at the intricate patterns of burned moth wings in the translucent glass of the overhead
light. Her father was in “hyper mode” again where nothing could calm him down.

The author of Touched, Jane Straus, wrote in the first chapter:

"Georgia went back to her bed and stared at the intricate patterns of burned moth wings in the translucent glass of the overhead
light. Her father was in “hyper mode” again where nothing could calm him down."


Is the first version without quotation marks the American way of punctuation, while the second is the British way?

Thanks.