The adhan tells you a prayer's time has begun. The iqama starts the congregation. They are different minutes, and the gap between them is a decision your masjid makes.
Adhan can be calculated
Adhan times come from astronomy. Given your location and the date, the position of the sun gives the start of Fajr, Dhuhr, Asr, Maghrib and Isha. Calculation methods use different angles for Fajr and Isha, so two careful apps can differ by a few minutes. Even so, it is arithmetic, and any app can do it.
Iqama is a local decision
Your masjid might pray Fajr 20 minutes after the adhan in summer and 30 in winter so families can arrive. It might hold Dhuhr at 1:15 pm all year because that suits workers from nearby offices. In Ramadan, Isha may wait for the crowd. No formula knows any of this. The imam or the board chose it.
Where apps go wrong
An app that only calculates shows you the adhan, and may guess the iqama by adding a fixed number of minutes. That guess fits a few masjids and misses most. Plan your drive around a wrong iqama and you arrive after the first rak'ah, or you wait outside for twenty minutes.
What MasjidNow does about it
In MasjidNow the masjid enters its own iqama and Jummah times. The app shows those times for the masjid you set as your default, and when the masjid changes one, you see the change.
There is one limit. The app is only as current as the masjid keeps it. If your masjid has not published its times, ask the board to add them. Listing a masjid and its times is free.
A habit worth keeping
Look at your masjid's iqama, not your city's adhan. Then set a reminder that counts back from iqama, which our guide on choosing your reminder time explains.