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There are some apps in the Google Playstore that promise simple data transfer from an old mobile phone to a new one. Unfortunately, it's not always very successful and it's a lot of trouble. The best results come from transfer processes that are directly integrated into the setup of new/old smartphones. Transfer apps from mobile phone manufacturers such as Samsung or Huawei are also good for transferring your data.
Data can be directly transferred from an android phone to a new iPhone during the setup process. For some manufacturers, it's a specific part of the setup process (e.g. Motorola). Other manufacturers offer their own transfer tool (e.g. the "Samsung Smart Switch" tool). Data transfer works both ways. Recommendation: make an updated backup before doing any kind of transfer.
The easiest option with an android device is synchronization and backup via Google. All data, pictures, contacts, etc. are transferred from your Google account to your new mobile phone via the cloud. Apple has something similar called iCloud which syncs your new iPhone to the "old condition". Usually, new Apple and android devices also have a feature to transfer data from an old mobile phone to a new device via WLAN. Another option is to transfer data between two mobile phones via Bluetooth or NFC.
The duration depends on the amount of data and the quality of the WLAN connection.
You can transfer data between two android phones using a cable if you have the necessary adapter to convert the charging cable into a transfer cable. In the transfer app, the "transmission path" isn't marked for WLAN, Bluetooth or NFC but it is for USB cable.