Before 1898, postage was 1¢ for an official Post Office card ("U.S. Postal Card") but 2¢ for a privately published card. Letter postage was also 2¢, so there was little motivation to use a private postcard rather than a letter. Only the address could be written on the address side of the card. As these examples show, cards were used for both personal and business purposes.
The Private Mailing Card Act of 5/19/1898 fixed domestic postage for all postal cards at 1¢, making privately issued cards competitive with Post Office cards. The Act required the back of each card to say "Private Mailing Card". The back could be used only for the address, so the front layout usually included ample blank space for a message. Many private mailing cards use a soft edge border around the image, resulting in a very distinctive look. The government relaxed the "Private Mailing Card" restriction on 12/24/1901, allowing cards to use "Post Card" on the back instead, so private mailing cards were only in use for a few years.
Detroit Photographic Co. was the most prominent national postcard publisher at the start of the 20th Century. Unlike most local publishers, Detroit used their own photos rather than photos purchased from local photographers.
Edward H. Mitchell (1867-1932) was a prolific local San Francisco postcard publisher from the late 1890s through the early 1920s. Multiview cards like these were popular in the early years of the 20th Century.
Mitchell's colored private mailing cards are typically of better quality than his poorly printed later cards.
Private mailing cards not shown above: Mitchell 58, Mitchell, S.F. Card 109, Unknown publisher 11. Gruber has a Private Mailing Card era back but it obviously post-dates the 1906 earthquake (per caption). The much later Mark Hopkins also identifies itself as a private mailing card, possibly because the hotel offers to stamp and mail it.
Steve's SF postcard pages: