About time

The 18th century lasted from 1701 to 1800 in the Gregorian calendar.

"The 1700's" and "the 18th century" are referring to the same block of time on the calendar.

many thanks O(∩_∩)O

It could be either one, you'd have to know from context. For example, one might read: "Johnson, who was unmarried as of 1699, recorded the birth of his son in 1711. He must have met his wife in the 1700s." This would be a very rare and unusual situation, however. I would say that, 999 times out of 1000, "1700s" refers to the first 99 yeas of the 18th century.

There is some ambiguity in when a century begins. I'd say in general usage people more often will say the 18th century was 1700-1799. People generally think the 21st century began in 2000. Others say centuries run from 1701 to 1800. That is based on the fact that in the Gregorian calendar there was no yeaqr zero between 1BCE and 1CE, so a priori the first century was 1-100 AD (or CE). This is an ongoing debate, though usually only around '00-'01 years. After that it mostly dies down. In any case, "the 1799's refers to any year that begins with 17, jnot just the first decade or two of the century.