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In general, analytics tools count users, but each analytics tool has its own way of counting. Sometimes, user counts can appear to be incorrect for various reasons, especially when measuring users over time.
If a user installs your app on Monday and then returns on Tuesday, a daily usage chart will show two users. But if you change the chart to cover both days, the chart should show only one user, since it was the same user both days.
This common source of confusion is called the Hotel Problem.
Different analytics tools also have different ways of looking at new users. Localytics views a user as new only the first time they open your app. So, a new user who opens your app twice in one day would appear twice in a new versus returning chart: as a new user for the first app open, and as a returning user for the second app open.
On most platforms, users are identified through IDs provided by their operating systems that persist between app installs. As a result, if a user deletes your app and then reinstalls it a week later, Localytics would still consider them a returning user. On top of the IDs provided by operating systems, Localytics also generates a separate stored identifier, so that if a platform changes the available identifiers during an upgrade, existing users are still detected as returning users.