A Relay is a Switch
Just like a light switch on the wall, all a relay does is connect two wires together, or disconnect the two wires. The wires are connected to the contacts, and the coil is an electromagnet. The electromagnet moves the common contact from the normally closed contact to the normally open contact.
Even though the relay diagrams look different, all three diagrams are for the same relay. One is a schematic diagram and the other two are wiring diagrams.
There are many ways to represent a relay on paper.
How the relay diagram is shown on paper depends on whether the diagram is to show signal flow, like when designing a circuit or fixing a circuit, or whether the diagram is to show how to land the wires, like when installing a system. Each way of representing relays in the diagrams has a purpose.
Form A, Form B, Form C
Often times, Form C relay contacts are specified. Form A, Form B, and Form C don't show the wiring outside the relay, the different "Forms" show the contact layouts inside the relay. Form A and Form B contacts are more limited than Form C, which can conduct electricity whether the relay is active or inactive. There are other "Forms" for different relays, but those other "Forms" are mostly for specialized functions.
Dry Contacts
The term "Dry" means "By itself, it doesn't provide any voltage or power". Dry really means that the contacts are only switch contacts.
When you see the term "Dry Contacts", it means that whoever said that is differentiating the relay from a "Wet Contacts" relay like a supervised output module in an addressable fire alarm system. A supervised output module provides supervision voltage.
In the case of an addressable supervised output module, the supervision voltage is on the screw terminal output of the relay module. The supervision voltage is on the screw terminals whether or not any wires are connected. If the relay contacts are dry, the relay, by itself, doesn't provide any voltage or power on the output terminals.
Relays are Switches
The common contact (sometimes referred to as "C" contact or "Comm" contact) in the relay is the contact that moves. Often, the common contact is referred to as a "Pole".

When there is one movable contact in the relay, the relay is said to have a "Single Pole". When the relay will conduct electricity when the movable contact is in either of two positions, the relay is a "Double Throw".
The above relay is a Single Pole Double Throw relay, or SPDT relay.

When there are two movable contacts in the relay, the relay has a "Double Pole".
The above is relay is a Double Pole Double Throw relay, or DPDT relay.
Many relays have more poles. Some are 4PDT, 6PDT, or 8PDT. I've even seen 24PDT relays.
Pictures of Relays
SPDT (Single Pole, Double Throw) Relay
4PDT Relay
8PDT Relay
DPDT Relay
The Difference Between Relays and Contactors
DPDT Contactor (Relay)
Mostly, the difference between a relay and a contactor is in the size. Physically, a contactor, which turns on and off the electricity using an electromagnet and contacts, is larger than a relay, which also turns on and off the electricity using an electromagnet and contacts.
Douglas Krantz