You can separate iMessages (blue bubbles) from standard SMS/MMS texts (green bubbles) by using the "Filter Unknown Senders" feature in Settings, or by managing iMessage Settings (like signing out or disabling iCloud sync) to control syncing across devices, but you can't completely split them into two separate apps; they'll always live in the same Messages app, just visually distinct by color and filters.
Steps
To ungroup objects, tap the group, then tap Ungroup.
On your iPhone, go to Settings. Tap Messages. Set iMessage to Off.
Go to Settings. Tap Messages. Turn iMessage off. Go back to Settings.
Check access permissions in settings
Spyware and monitoring apps need elevated permissions to access your SMS messages. You can check whether any apps have permission to see your SMS messages by going to the Permission manager in your Android settings.
iCloud exploitation
Your iCloud account is a gateway to all your synced data, including text messages. Someone can spy on your messages by: Logging into your iCloud account from another device to view message backups. Using a shared Apple ID (common in families) to receive your iMessages on their device.
What happens when I turn off iMessage? Your messages will be sent as SMS instead of iMessages. You'll no longer see the blue message bubbles—just green ones.
Set up Dual SIM
Disabling iMessage means all incoming messages, even iMessages from fellow Apple users, are supposed to arrive in the standard SMS text format. However, If you enabled iMessage across multiple Apple devices, disabling iMessage on one device won't disable it for all of them.
SMS offers a much greater reach than iMessages because SMS can reach all mobile phones (and other text-enabled devices), irrespective of whether the operating system is Android or iOS. That's why SMS is used as the fallback channel when iMessages fail to deliver over WiFi or mobile data.
Open Settings on your iPhone. Scroll until you reach the Messages option. Once here, ensure iMessage is selected. If not selected, enable that.
Turn your phone number on or off for your Mac
For Messages, choose Messages, select Settings, then click iMessage. For FaceTime, choose FaceTime, select Settings, then click General. Turn your phone number on or off: To turn on your phone number, select it and your Apple Account in the list.
This typically happens when you text someone who isn't using an Apple device or when iMessage is turned off. Poor internet connection, iMessage activation issues, or software glitches can also be the cause.
Tap the group icons at the top of the thread. In the list of contacts, tap and hold the person you want to remove. Tap Remove from Group, then tap Remove.
Change how you send group messages
Under 'Settings: Messages: Group Messaging' there is an option to disable.