It depends on the director and the crew's capability, as well as the actor's ability to act with or without an audible cue.
You can have a regular phone hooked up to a regular phone line or PBX and then ring it by calling it or it's extension.
- Authentic sound
- Not as easy to time
- Provides cue for actors
- Actors can listen and speak to person on other side - perhaps boths sides can be recorded, but also it encourages natural pacing even if only one side ends up on film.
You can have the actors act as though it rung, answer it, and add it in post production.
- Timing is easier, but depends on actor's ability
- Depends on actor's ability to convey a normal reaction to an unexpected sound
- Sound timing can be very precisely managed in post
You can buy phones that ring on cue.
- Similar to a real phone, but doesn't require a phone line or PBX
- Specialized device, can't always choose the phone you want to use
You can buy devices that ring phones for you by applying the correct signals on the phone line.
- Can use any standard phone, even decades old since the standard has been around for so long. This gives the director more options, and they can rent a phone from a prop company and don't have to modify it.
- Some allow two phones and recording both sides.
- Accurate ring - it's actually that phone's ring
- Precise in-camera timing (depends on person activating it, but there are no delays like you might have with a PBX or real phone line)
For cell phones you can do nearly all the above as well.
You can use an active, real cell phone in the scene and call it.
- Accurate sound, accurate screen images
- Can't control timing as well
- Have to be careful phone doesn't operate inadvertently at other times
- usually a dedicated prop phone and phone number that's unpublished, with few to no apps and other notifications turned off
- Can interact with it normally, including declining the call, adding additional callers to the call, etc
- Can be used for texting as well
- Must be managed more carefully - battery dying at the wrong time could scratch a take, and could take time to charge and reset the scene.
You can use a real cell phone but only pretend to answer it and add sound in the post.
- More accurate timing of ring
- Screen won't reflect what's happening (unless modified in post)
- More common for older style analog cell phones which are harder to get attached to today's networks (late 90's or early 2000's period pieces)
- If there's a display the actor may need to use the phone in a way and at an angle that prevents the display from showing on camera which can be done well, or poorly.
- Depends on actors similar to the non-ringing regular phone above
You can use a fake cell phone with a screen dummy that allows both sound and CGI to be added in post so the display operates as the director wants it to.
- Prop is more durable than a real phone
- Timing of both display and sound very precisely controlled in post
- Requires more post production, but with a green screen and markers on the display face this isn't the chore that it used to be.
A lot of this comes down to the effect the director wants, the capability of the actors, and the capability of the effects crews that would be involved. There are always other methods, this is just a simple overview.