Select Move from the Block menu to delete the selected text and insert it again at the current position of the text cursor. Block|Move will only become enabled when you have enabled persistent selections in the Editor Preferences. Only when selections are persistent, you can move the text cursor without clearing the selection.
Selecting text, moving the text cursor, and invoking Block|Move has the same effect as selecting text, invoking Edit|Cut, moving the text cursor, and invoking Edit|Paste. The only difference is that Block|Move does not use the clipboard, so the contents of the clipboard are preserved.
The option "paste whole lines when lines are copied as a whole" affects how text is moved when you have selected complete lines. Selecting a complete line means to select everything from the start of the line to the end of the line, including the line break at the end of the line. Selecting multiple lines completely means selecting everything from the start of the first line in the block until the end of the last line in the block, including the line break at the end of the last line. When the option "paste whole lines when lines are copied as a whole" is on, whole lines are always moved as if the cursor were at the start of the line when you invoke Block|Move. Thus, whole lines are always moved as a whole before the line that the cursor is on when moving. This makes it easy to move blocks of lines without worrying about the horizontal position of the text cursor. If this option is off, the selected lines are moved to the exact spot the text cursor is at, even when whole lines are selected.
If you use the menu item or toolbar button to invoke this command, it will be invoked on EditPad's main editor, where you edit files. If you press the shortcut key on the keyboard, it will be invoked on whichever editor is showing the text cursor (vertical blinking bar), whether that's the main editor, the search box or the replace box.