Moving cards from the field, Graveyard, Banished Zone, or Extra Deck to the hand; moving a card to the Extra Deck (face-down) or the Main Deck; moving a banished card to the Graveyard; and moving a temporarily banished card back where it was originally with the effect that banished it are all forms of returning.
Returning to the hand or Deck
Shuffling a card into the Main Deck and placing a card on the top or bottom of the Main Deck are both forms of returning to the Main Deck (unless they were put there from the Main Deck). Shuffling a card into the Extra Deck is also a form of returning to the Extra Deck. Adding a banished card or a card from the Graveyard to the hand is a form of returning.
When a monster is destroyed by battle during the Damage Step, it cannot be returned from the field to the hand, Deck, or Extra Deck (unless a card effect specifically permits it, such as "Grave Protector"). When a Normal, Quick-Play or Ritual Spell Card, or a Normal or Counter Trap Card is activated, it cannot be returned from the field to the hand or Deck during that Chain unless it has an effect that would cause it to remain on the field after activation, such as "Swords of Revealing Light" or "Kunai with Chain" (unless a card effect specifically permits it, such as "Goblin Out of the Frying Pan").
Returning banished cards to the Graveyard
When returning banished cards to the Graveyard, returning is not considered to be sending a card to the Graveyard. Thus, cards like "Miracle Dig" and "Fortune's Future" can be used to return monsters to the Graveyard even if "Macro Cosmos" is active; the returned cards will not be banished again.
Returning temporarily banished cards
If a monster is temporarily banished from the field, such as by "Interdimensional Matter Transporter" or "Ninjitsu Art of Shadow Sealing", it is not Summoned when it is returned to the field. Whether or not it will be destroyed by "Jowgen the Spiritualist" depends on how it was originally Summoned. If a temporarily banished monster would return to the field but there is no free Monster Zone, it is sent to the Graveyard.