There are, under US law, two separate copyrights (at least) in any musical recording. The first is the copyright on the recording itself. The second is is the copyright on the musical composition that is being recorded. If that composition is an arrangement or modification of an original, there will be a separate copyright on the original, as well.
The copyright on the performance will be initially held by the musicians, but may have been signed over or sold to a recording company or someone else. If the performance was recorded before 1972, there will be no copyright under US Federal law, but there may be limited protection under state law.
The copyright on the composition, and on the arrangement if any, has terms basically the same as on a printed work. Works published before 1923 will be in the public domain. Later works may have a term of 95 years, or 70 years after the death of the author. See the cornell chart for details. Such copyrights are initially owned by the composer or composers, and possibly the writer of the lyrics, or in some cases the employer of the composer(s)/lyricist(s). They may well have been sold or transferred and be owned by some company.
The exact rules will differ under the laws of other countries, but the general structure is much the same, i understand.
To use a recording you must obtain permission (a license) for the recording itself, for the composition (unless it is out of copyright) and for any arrangement (unless the arrangement is out of copyright). Performing rights societies are how professional performers and venues usually secure such rights. They charge fees which depend on the use someone wants to make. They offer licenses to a variety of music for a single payment.
A recording released under a creative commons license may or may not include a license for the underlying composition. Often it does not. Also, someone who uploads a recording to an online site such as YouTube stating that it has a creative commons license, may be lying, have no rights to the recording at all, and expose any reusers to the chance of lawsuit. If you want to use and reproduce such recordings, you must verify that you have proper licenses from all copyright holders.
The site Jamendo says that it offers "royalty free" music for various purposes. It says that the recordings it offers have all needed rights included. It charges various fees depending on the kind of license purchased, with discounts for bulk purchases. It offers a guarantee against claims of infringement by 3rd parties, but the terms seem to make this guarantee quite limited. It appears that for use in an online/mobile app, one must purchase their 'large" license or higher. Its terms do not seem to be compatible with creative commons licenses. I know nothing about this site, or its reputation, beyond what it says of itself.
Most of its licenses seem to permit creation of derivative works with the licensed music part of an audiovisual or multimedia work, but not the unaltered distribution of the music by itself.
I am not a lawyer, and this is not legal advice. Specifics matter in copyright cases. The above are only general principles.