"The 1800s" typically refers to the years 1800-1809. "The 1900s" refers to 1900-1909. It is by no means unambiguous, but this is the common and plain meaning, and indeed these folks may confuse many more people by attempting in this manner to refer to 1800-1899 or such.
I disagree. When people typically pronounce, for example, "1800s," they would say "Eighteen Hundreds," with the plural suffixing "hundred," implying a period of far longer than a decade. If trying to reference the decade following 1800, in conversation I would say "the Eighteen Noughts."
I don't know what sort of localized English you speak, but that is not how it works in America. [Based on past comments, you may be located in Australia. I could certainly understand if there are local phenomena in your language there.]
If we say "In the nineteen hundreds..." we mean 1900-1910. If we said "In the ninteen fifties" we would not be implying a 50-year period, would we? If we said "In the nineteen nineties" are we implying a 90-year period? Do you see how your logic immediately breaks down? Is it mere accident that "the ninteen tens" is a ten-year period of time? Yes it is...
Your assertions and these patterns of speech are just bizarre. I don't know anyone who says, or writes, "the Eighteen Noughts" at all. It is not a thing for scholars of history, for sure.
For a while it has been debated how we'll refer to 2000-2009. Because in different centuries, those initial ten years gained unique names. Some people want to call it "The Aughts" or "The Noughts" but I don't really hear people referring to "The Two Thousands" yet, at all; it's largely "The 21st Century".
"The 1800s" typically refers to the years 1800-1809. "The 1900s" refers to 1900-1909. It is by no means unambiguous, but this is the common and plain meaning, and indeed these folks may confuse many more people by attempting in this manner to refer to 1800-1899 or such.