Whats is the different beween Western European (Windows)-1252 and ANSI encoding

Cygwin or GnuWin32 provide Unix tools like iconv and dos2unix (and unix2dos). Under Unix/Linux/Cygwin, you'll want to use "windows-1252" as the encoding instead of ANSI (see below). (Unless you know your system is using a codepage other than 1252 as its default codepage, in which case you'll need to tell iconv the right codepage to translate from.)

Convert from one (-f) to the other (-t) with:

$ iconv -f windows-1252 -t utf-8 infile > outfile

Or in a find-all-and-conquer form:

## this will clobber the original files!
$ find . -name '*.txt' -exec iconv --verbose -f windows-1252 -t utf-8 {} \> {} \;

Alternatively:

## this will clobber the original files!
$ find . -name '*.txt' -exec iconv --verbose -f windows-1252 -t utf-8 -o {} {} \;

This question has been asked many times on this site, so here's some additional information about "ANSI". In an answer to a related question, CesarB mentions:

There are several encodings which are called "ANSI" in Windows. In fact, ANSI is a misnomer. iconv has no way of guessing which you want.

The ANSI encoding is the encoding used by the "A" functions in the Windows API (the "W" functions use UTF-16). Which encoding it corresponds to usually depends on your Windows system language. The most common is CP 1252 (also known as Windows-1252). So, when your editor says ANSI, it is meaning "whatever the API functions use as the default ANSI encoding", which is the default non-Unicode encoding used in your system (and thus usually the one which is used for text files).

The page he links to gives this historical tidbit (quoted from a Microsoft PDF) on the origins of CP 1252 and ISO-8859-1, another oft-used encoding:

[...] this comes from the fact that the Windows code page 1252 was originally based on an ANSI draft, which became ISO Standard 8859-1. However, in adding code points to the range reserved for control codes in the ISO standard, the Windows code page 1252 and subsequent Windows code pages originally based on the ISO 8859-x series deviated from ISO. To this day, it is not uncommon to have the development community, both within and outside of Microsoft, confuse the 8859-1 code page with Windows 1252, as well as see "ANSI" or "A" used to signify Windows code page support.

In Linux UTF8 is usually saved without BOM since UTF8 BOM is optional, thus apps might have problem detecting proper encoding. You can try to save them in UTF8 with BOM or use UTF16 instead.