From
The Bridge World Dictionary:
marionette
(1) (noun) a transfer (meaning 2), after which partner will usually make the cheapest bid but is permitted to bid higher with special hands. (Compare with puppet.)
(2) (verb) to use a marionette (meaning 1)
puppet
(1) (noun) transfer (meaning 2) [= a call that asks partner to make a certain call regardless of his holding]
(2) (verb) to use a puppet (meaning 1)
relay
(1) (noun) an artificial call, very often the cheapest bid, possibly nondescriptive or at most partially descriptive, that asks or allows partner to offer a description
(2) (verb) to use a relay (meaning 1)
(3) (adjective for system) a bidding method in which a high proportion of constructive auctions make use of relays
Examples of meaning (1) (the lettered calls are relays):
SOUTH WEST NORTH EAST
1 NT Pass 2 ♣(a)
(a) Stayman; asks opener for information without directly describing responder's hand. Some relays are more descriptive than others; for example, a two-diamond response to one-notrump might be game-forcing Stayman.
SOUTH WEST NORTH EAST
1 NT Pass 2 ♦* Pass
2 ♥(b)
*transfer to hearts (Jacoby transfer)
(b) completion of transfer; says little (in some contexts nothing) about the South hand
SOUTH WEST NORTH EAST
1 NT Pass 4 ♦* Pass
4 ♥©
*puppet to four hearts (Texas transfer)
© completion of transfer; says nothing about the South hand
Similarly, the expected reply to any puppet acts as a relay.
SOUTH WEST NORTH EAST
2 ♣ Pass 2 ♦ Pass
2 ♥* Pass 2 ♠(d)
*Birthright: either hearts or a game-going balanced hand
(d) relay enabling opener to clarify hand-type (by bidding either two notrump if balanced or higher with hearts)
transfer
(1) (noun) a bid that shows length in a different suit
(2) (noun) a call that asks partner to make a certain call regardless of his holding; [In this usage, also called Puppet.]
(3) (verb) to use a transfer (meaning 1)
(4) (verb) to remove protection in a suit from one opponent and give it to the other
(5) (adjective) a squeeze involving a transfer (meaning 4)