There's one press but two types of newspaper:
The broadsheets are the larger and more serious papers.
The tabloids are the smaller and less serious newspapers full of celebrity scandals, etc. :lol:
PS, there is an old term 'Yellow Press' for the scandalous type of newspaper, but it isn't used much nowadays. As an insult, you also here the phrase 'gutter press' and some people call the tabloids 'Red Tops'.