I believe this is primarily a difference between American English and British/Australian English. American English usually includes the period (e.g., St. Patrick's Cathedral in New York or St. Paul, Minnesota) whereas British and Australian English typically omits it (e.g., St Paul's Cathedral in London).
Telegram style, telegraph style, telegraphic style or telegraphese describes a clipped way of writing that attempts to abbreviate words and pack as much information into the smallest possible number of words and/or characters.
It originated in the telegraph age when telecommunication consisted only of short messages transmitted by hand over the telegraph wire. The telegraph companies charged for their service by the number of words in a message, with a maximum of 15 characters per word for a plain-language telegram, and 10 per word for one written in code. The style developed to minimize costs but still convey the message clearly and unambiguously.
Of the four names mentioned, telegraphic style is the version that I'm familiar with.
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Found it in another question: North American English
Why some abbreviations ended with a period, but some not?