To see the difference you need to give tkinter a reason to not fit the cell exactly around your widget, which it will always do by default if possible. Try:
from tkinter import *
from tkinter import ttk
root = Tk()
root.rowconfigure(0,weight = 1)
root.columnconfigure(0,weight = 1)
frame = ttk.Frame(root)
frame.grid(row = 0,column =0)
ttk.Label(frame,text = 'Label_1',background='red').grid(row=0,column=0,sticky='nwes')
ttk.Button(frame,text = 'Button').grid(row=0,column=1,sticky='nwse')
ttk.Label(frame,text = 'Label``_2').grid(row=0,column=2,sticky='nwes')
ttk.Label(frame,text = 'LOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOONNNNNNNNNNNNNNNNNNNNNNNNNNNNNNGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG').grid(row=1,column=0)
root.mainloop()
and next remove ,sticky='news' from Label_1. Note that the text centering and widget centering are two different things - that's why I gave a background color, to make it evident.
Also, you do not really need ttk, you get your Buttons and Frames from from tkinter import * already, though I would explicitly list them as in from tkinter import Button,Frame,Tk or use import tkinter as tk and use tk.Label.