There are three basic groups of clocks that are common today:
1) Mechanical clocks that rely on an escapement wheel and spring or a pendulum to count out intervals of time. These have been around in various forms for several hundred years. There are also some less common variants that rely on these of similar timing mechanisms.
2) There are clocks based around some form of electronic circuitry that relies of the resonance of a quartz crystal or a tuning fork to measure time. These tend to be much more accurate than the purely mechanical clocks.
3) There are clocks that rely on time measured by atomic clocks, relying on the characteristics of caesium-133 or the rubidium-87 atoms for very accurate time keeping. Even these are not 100% accurate, and a network of atomic clocks in different institutions around the planet are compared and synchronised to provide a single universal time reference. It is impractical for private individuals to have their own atomic clocks, so various radio time signals are broadcast around the planet from which personal clocks and watches can get their time settings.
These private secondary time pieces that derive their time by radio from national time standard do not normally receive the signal continuously. They turn on their receivers perhaps once to four times a day and adjust themselves to the broadcast time at that point, then rely on a local quartz crystal timer to maintain a reasonable time reading until the next synchronisation time.
So those are the three main groups. Within each group there can be time pieces that display time either on an analogue display or on a digital display.
In the three groups listed above, the first tends to be the worst for maintaining accurate time, and the third should always be the best as this effectively is the definition of time for the whole planet.
There are other ways besides radio signals that time can be passed on. Telephone caller displays typically receive a signal from the phone company specifying the hour and minute that a particular call arrived. Normally caller displays do not use seconds, so their clocks can vary by up to a minute. Mains powered clocks often use the frequency of the mains power as the reference, and these can gain and lose several times a day as the load on the power network varies. Although short term, these clocks may vary by a minute or two, averaged over several weeks, they normally keep excellent time as a long term figure. Some mains powered clocks have a battery backup to keep them going over a power cut. This is often a very crude oscillator and when the mains power is off for some time, the clock can be wrong by several minutes when power is restored. Since the mains does not actually carry a specific time signal, a mains powered clock that is accurate as long as power is present will not go back to the correct time after a power outage. All the mains is providing is a count frequency, but no reference to any specific time.
Your laptop will periodically request its time from a time standard over the Internet. Windows systems tend to do this once a week, and rely on a quartz crystal based clock on the laptop's motherboard to maintain time between the weekly Internet checks.
A mechanical clock can vary in accuracy from a few seconds a day to several minutes per hour.
A tuning fork or quartz crystal devices should be able to stay within 2 seconds a day, although cheaper ones may not be close to this figure.
Clocks and watches that rely of radio signals for their time should stay within one or two seconds providing they are in range of the appropriate radio signals.
As I said before, whether it is a digital or analogue display should make not difference. The time measurement and the actual display mechanism are two separate aspects of a clock.
I hope this helps.