Technically, music coming from your local storage or from the interwebs are both streaming. 
If your stored music is stored as .wav or uncompressed .flac format then hearing the difference isn't unusual. I believe the Qobuz stream is a compressed flac file. It requires more processing power to unfold the file on the fly as opposed to playing the uncompressed file. If your stored files are also compressed flac I have no idea why they sound different. How does your cd transport compare to the streaming, both local and from the interwebs?
Need to clarify what type of "compression" is being referred to here.
1) Compression of the music file/container: Example, the WAV format is uncompressed. FLAC is "lossless compression": the FLAC file is smaller than the source uncompressed WAV file, but the compression method used does not remove any parts (bits) from the source file to achieve compression. The sound qualify of the FLAC and WAV files are the same. (The "processing power to unfold the (FLAC) file" is really no longer an issue. It might have been an issue with an old Pentium PC with 16 MEG of RAM, but more modern PC's will not be taxed decompressing compressed music files.) MP3 files use "lossy compression": the compression methodology discards elements (bits) from the source file to achieve a reduced file size. Its not uncommon for individuals to hear a difference between an uncompressed source file and a an MP3 file.
2) Compression as applied during the mixing/mastering process: this may account for different releases of the same recording sounding different. For example, assume that Columbia Records decides to re-release a recording of "Joe's Band" (fictional band) from 1975. In 1975, the original recording was saved to a "master tape" (or more than one master was saved for archival purposes). That master tape may have been pulled from storage, played back and "re-recorded" using digital recording equipment. So, when Columbia decides to rerelease the 1975 recording from Joe's Band, the mastering engineer might have access to only the digital re-recording. If the engineer has access to both the analog master and the digital master, they could choose either based on the engineer's preference (or, possibly Columbia's marketing preferences - Columbia may want to market the re-release as "sourced from the original master tapes"). From there, the engineer applies their experience and preferences for achieving the best possible sound for the release. It could include reducing or increasing one or more frequencies of the original. It could also involve applying dynamic compression in the studio: a technique that reduces the distance in dbs between the loudest and quietest parts of the recording. This compression technique has become more prevalent in recent years.
3) Compression that may be applied by the streaming service. This compression is applied to the music that is streamed from the music service based on the subscription level of the subscriber. Example: Deezer Free users experience compression at 64kbps or 128kbps, while Premium users stream at a higher quality with MP3 compression up to 320kbps. Deezer Hi-Fi subscribers receive lossless FLAC streaming at 16-bit, 1,411 kbps.
So, back to a locally stored music collection, and why the same recording might sound different when played back via your local server versus a music stream like Qobuz: I suspect the difference you're hearing is:
1) Unrelated to #1. The lossless container would not impact the sound quality. There are endless debates on this, and "audiophiles" who insist they can her a difference between uncompressed WAV and compressed FLAC. I can only tell you what the science states, and my own experience - there's no difference.
2) #2 could be a significant contributor to differences in perceived sound quality. Quboz might be playing a "re-mastered" version of a recording. If you own the original recording and listen to both the remastered and the original for comparison, it's quite possible that the recordings will sound a bit different. Whether one version is "better" than another is in the "ear of the beholder".
3) #3 could definitely be a contributor in some circumstances. If comparing music streamed from Spotify to your current lossless music collection, hearing a difference based on the type/level of compression that the music service uses would not be surprising. In the case of Qobuz, I suspect that this would not be a factor.
One last item, and this is a bit of a "rant": its difficult to attribute differences in sound quality when listening to streamed music. Heck,. there are "audiophiles" who proclaim vast differences in perceived sound quality just by changing the interconnect cables between their CD player and their preamp, or the power cable between their amp and the electrical outlet. Stop for a second to consider how the music that is played back from a service like Qobuz arrives to your speakers. What does that signal path look like? How many individual service providers exist between Qobuz and you?
Consider a fictional streaming music service: X Music. X Music is streaming service provider. Their servers might be self-hosted, or they might (#1) outsource their server capability to another service provider to host their IT infrastructure. There may be another service provider (#2) that connects that host to the internet. That signal may then travel to another server farm that (#3) that works with your ISP (#4) from whom you purchase your internet service. Your ISP introduces a couple more variables (#5): is your internet signal transmitted via fiber optic or coaxial cable? Does distance (#6) between your ISP's server hub and the ISP's connection to your home play a role in signal quality. Or (#7) are you an early adopter of home internet via 5G cellular connection? Did your ISP provide you with a high quality router (#8)? Is the connection from the router to your streamer and/or DAC (#9) thoroughly galvanically isolated?
Given all the roads that X Music's signal must travel, and all the hoops that signal must jump through, to get to your speakers, is it reasonable to assume that no degradation in sound quality is possible? Compare that assumption to the folks that insist that changing an electrical cable in their system made audible improvements, and I suspect you get my meaning.
