Are there any special words or phrases for people that were emigrating in history (18th, 19th, 20th centuries)? Or maybe the words which were used in that time and how were people calling the emigrants? Anything related to that would be very helpful.
The earliest reference in the OED (Oxford English Dictionary) to the verb emigrate is from 1782.
1782 T. Pownall Treat. Study Antiq. 60 (T.) The surplus parts of this plethorick [printed phletorick] body must emigrate.
The OED's Historical Thesaurus, which is a wonderful new tool for historians of the language, published in 2009, suggests the following synonyms, with dates:
remove 1388; flit 1504; shift 1530; to pull up stakes (US) 1703; move 1707; emigrate 1841; uproot 1961; pick up stakes (US) 1974.
The settlers had come to America to look for land
Etymonline says that the term settler, meaning a person who moves to a different land or country is dated from the 1690s, which makes it older than the verb emigrate
1590s, "a thing that settles" (a debate, etc.); agent noun from settle (v.). Meaning "a person who moves into a new country" is from 1690s.