The reason why the second one appends and the first one doesn't, is because of the $FileHandle = fopen("MyFile.txt", 'a+') or die("Cant open file!");
line.
Notice the a+? That means: append & read.
w3schools has a list of all opening types (by the lack of better words, lol) available here
r Read only. Starts at the beginning of the file
r+ Read/Write. Starts at the beginning of the file
w Write only. Opens and clears the contents of file; or creates a new file if it doesn't exist
w+ Read/Write. Opens and clears the contents of file; or creates a new file if it doesn't exist
a Append. Opens and writes to the end of the file or creates a new file if it doesn't exist
a+ Read/Append. Preserves file content by writing to the end of the file
x Write only. Creates a new file. Returns FALSE and an error if file already exists
x+ Read/Write. Creates a new file. Returns FALSE and an error if file already exists
One less click!