To my knowledge there are six types of legal offline music apps in the App Store:
'FREE':
1. 'free' with ads and sometimes other limitations or additional in-app purchases to get further functionality: Trebel Music, Current Rewards: Music Player, Audiomack, DatPiff, My Mixtapez Music, Jamendo Music (creative commons music only)
2. free: podcast apps where you can subscribe to music podcasts (not individual songs) e.g. Pocket Casts
3. free (with ads or pay once): your own music collection that you download from your cloud storage CloudBeats
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PAID:
4. with a pay once option: - various podcast apps where you can subscribe to music podcasts (not individual songs) iCatcher (podcast only, 2.99 euro once), hearthis.at (mixes only, 2.99 euro once)
5. with a subscription (all the big names such as Spotify, Apple Music, Pandora which are mostly 9.99 euro a month or smartradio offline: 3.99 - 5.99 euro a month: Pandora, LivexLive, iHeart, SoundCloud Go, Mixcloud Select 2.99 euro a month only one artist offline)
6. included in another subscription: Amazon Prime Music (free limited database is available in some countries with Prime subscription), YouTube (Music), Apple Music (included with Apple One subscription)