As it pertains to stereo, basically a difference in nomenclature, but could be slight variances, people will argue the sound quality for eons. It is Apple's lossless ALAC codec versus Tidal's MQA codec. Atmos is is a separate codec from ALAC or MQA and it currently is not lossless, they use DD+ as does Tidal.
Apple Music-
When you listen in stereo it is lossless. Lossless compression is a form of compression that preserves all of the original data. From Apple's website: "Apple has developed its own lossless audio compression technology called Apple Lossless Audio Codec (ALAC). In addition to AAC, the entire Apple Music catalog is now also encoded using ALAC in resolutions ranging from 16-bit/44.1 kHz (CD Quality) up to 24-bit/192 kHz."
Tidal-
Tidal Masters uses MQA technology for the stereo version, from Tidal's website: "HiFi audio is a superior sound but is still limited in its resolution—44.1 kHz /16 bit. TIDAL has partnered with MQA to deliver something substantially better: an authenticated and unbroken version (typically 96 kHz / 24 bit) with the highest possible resolution—as flawless as it sounded in the mastering suite. And exactly as the artist intended it to sound. Original master recordings - authenticated by the record label or artist themselves. Unrivaled quality, clarity and depth delivering all file sizes (up to 24 bit / 352kHz), using no more bandwidth than a CD quality (16 bit / 44.1kHZ) file (up to 9216 Kbps or 24 bit / 192 kHz)."
Caveat with Tidal Masters -
you need a DAC that can decode MQA to get the "full" MQA quality: "While TIDAL on iOS and Android can unfold part of the audio source natively, allowing for an enhanced listening experience by default, using a DAC will unlock its full potential and give you optimal performance."
For Atmos on Tidal: "
Immersive Audio - Allows sounds to be precisely and spatially placed. We are the only service to support both
360 Reality Audio and
Dolby Atmos on mobile devices."