Yes, technically a solenoid is ANY coil of wire used to create a uniform magnetic field within that coil's space
And under that basic definition an ignition coil(for spark) could be called a solenoid, but it isn't called a solenoid
As with all things function changes its name
We have stairs inside the house but steps outside??? WTF.........LOL
So if this magnetic field is generated to move something, like washing machine's water valves or starter motor gear its called a Solenoid
If magnetic field is generated to make an electrical connection its a Relay
If magnetic field is generated to make a spark its an ignition coil
On some starter motors there is a combo unit, a solenoid/relay, because it does BOTH functions, moves starter gear out and connects battery positive cable to the starter motor's brushes
If its in a fuse box or on the inner fender its a relay, but inner fender unit was called a solenoid for years PRIOR TO relays being used in vehicles
But Relays are used now, so welcome to the PRESENT