DIRECT ANSWER
Two prayer apps disagree because they use different calculation methods: mainly different sun angles for Fajr and Isha, a madhab difference for Asr, and different rules for high latitudes. The gap is usually 1 to 5 minutes, and neither app is "broken". An app for a specific country should use that country's official method or its published times.
What actually differs between calculation methods?
Three things differ between methods, listed below:
- Fajr and Isha angles. Both depend on twilight, when the sun sits below the horizon, so each method fixes an angle: some use 18 degrees for both, others 15, others mix (for example 18 for Fajr and 17 for Isha). A steeper angle means earlier Fajr and later Isha.
- The Asr shadow ratio. In the Shafi'i, Maliki, and Hanbali schools, Asr begins when an object's shadow equals its length. In the Hanafi school, Asr begins at twice the length. That single ratio moves Asr by tens of minutes.
- High-latitude adjustment. Above roughly 48 degrees latitude, true twilight can persist all night in summer, so methods substitute rules such as the nearest valid day or a fixed portion of the night. Apps that skip this show impossible times in northern Europe.
Dhuhr, Maghrib, and sunrise barely differ between methods, because the sun is visible at those moments and the astronomy is not in dispute.
Which calculation method should an app use?
The method should follow the user's country, not the developer's preference. Major methods are tied to regions and authorities: the Muslim World League, the Egyptian General Authority, Umm al-Qura for Saudi Arabia, the University of Islamic Sciences Karachi, and ISNA for North America. A well-built app detects the country and defaults to the locally accepted method, then lets the user override it. An app that hard-codes one global method is quietly wrong for most of the world.
Why is official authority data better than calculating?
Where a national authority publishes official times, using them beats computing your own. Malaysia is the clear case: JAKIM's e-Solat publishes times for all 60 zones, and those are the times every mosque follows. An app that calculates its own Malaysian times can drift a minute or two from the mosque next door, which users read as the app being wrong, because for their purposes it is. DuaLab's Takbir serves JAKIM's published data directly for exactly this reason, and the same source-over-calculation decision applies to any country with an official authority. Building in this category? See Islamic prayer app development.