Relay is an electromagnetic operated switch.. An electromagnetic coil with a combination of mechanically linked contact points that are mounted on a spring loaded lever which pivots on a hinge-like mechanism on the side of an electromagnetic coil. A mechanically linked combinations of normally open and normally closed switches as the lever gets attracted by the coil when energized

Solenoids on the other hand is an electromagnetic coil with a hollow center core where a spring loaded rod, a solenoid plunger is passed thru. The plunger action moves up and down inside the hollow core when the magnet is energized. The tip end of the plunger most of the time is mechanically linked to a valve, or a switch.. for an open and close operations..

The possible difference are in the applications which is mainly due to the way the mechanical linkage was designed and implemented..

Relay applications are mostly in switching electrical energies, to handle larger amount of current or for automation, where a given tasks or routine are automatically switched as programmed..

Solenoids are mostly used for switching controls of mostly hydraulics and pneumatics applications, both for manual programmed programmed automations processes.

Relay

Solenoid

What do we find in common, Yes both has winding and it they are Energized they get magnetized and give out some mechanical movement.

Now A relay act as a switch (Only as a switch) with the aid of this mechanical movement.

A Solenoid will use this mechanical movement to actuate a valve or a door. You can refer Solenoid valve for a clear understanding.

NOTE: Only Electromagnetic Relay will have winding in them.

References:

https://www.quora.com/What-are-the-differences-between-a-relay-and-solenoid

https://www.powerelectronictips.com/solenoids-relays-part-1-faq/

https://www.quora.com/What-is-the-different-between-solenoid-and-a-relay

https://www.youtube.com/watch?v=i3lGy3MjUhY

https://physics.stackexchange.com/questions/203762/flemings-right-hand-and-left-hand-rule