All song cycles might have an opus (Latin for "work") number, but not all pieces with opus numbes are song cycles. Symphonies, concerti, sonatas, tone poems, etc., might all have opus numbers, but none of those are song cycles.
A song cycle is a collection of songs intended to be performed together. Often the songs will have a common theme or they might tell a story when performed or heard together.
A song is a musical work that is focused on one or more vocal parts, usually vocals that have lyrics (sung words). Not all pieces that have vocals would be considered songs, but all songs feature the vocals.
For example, the 14th piano sonata composed by Ludwig Von Beethoven is called "Sonata number 14" and it's also called "Opus 27, number 2", because it is the second half of his 27th work overall. That means that about half of his works numbered Opus 1-26 are piano sonatas (i.e., sonatas 1 through 13), and half of them are something else. A piano sonata is a work written for solo piano that is divided into movements. Since there is no singing in a piano sonata, it is not a song, and would never be part of a song cycle.