The correct spelling of the first term is "bâtonnage"; but
misspellings of this French word are used very often, "batonages"
being one of them.
"Bâtonnage" is the process of stirring the dregs (dead yeast and grape
residues) in a vine by means of a stick ("bâton" in French). This is
done while the wine is aging in its container, after the end of
The purpose of the bâtonnage is to support the autolysis of the
yeasts, thus giving more body to the wine, and to support the
development of complex flavours.
The second term, "délestage", means a complicated process where the
wine is withdrawn from its containers during fermentation and then
returned again. This procedure not only makes the wine age faster, it
is also used to control and improve taste and color. You can read a
detailed description here, at Wine Business Monthly:
Hope this answers your question!
Wikipedia: Bâtonnage (in French)
Wine Business Online: Delestage - An Attempt to Balance Flavor and Finish
Le Domaine du Temple: Glossary