Correct. DCT maps N real numbers to N real numbers. It reorganizes the data to make it more amenable to compression, but DCT itself doesn't do any compression.

The real compression comes from quantization and entropy coding (Huffman coding, arithmetic coding, etc.).

> DCT compression, also known as block compression, compresses data in sets of discrete DCT blocks.[3] DCT blocks sizes including 8x8 pixels for the standard DCT, and varied integer DCT sizes between 4x4 and 32x32 pixels.[1][4] The DCT has a strong energy compaction property,[5][6] capable of achieving high quality at high data compression ratios.[7][8] However, blocky compression artifacts can appear when heavy DCT compression is applied.

https://en.wikipedia.org/wiki/Discrete_cosine_transform

Exactly, it’s not an algorithm, it’s one mechanism used in many (most?) compression algorithms.

Therefore, it has no compression ratio, and it doesn’t make sense to compare it to other algorithms.