Regular COVID tests are able to detect both the Delta variant and Omicron variant in that they can determine whether or not you have the coronavirus. However, they can't tell which variation is involved. That would necessitate genomic sequencing, which is a different process from regular virus testing that not all labs can undertake. Sequencing is uncommon and can cost up to $100 per test. Since the treatment is the same for any variant, it is not clinically useful to an individual patient to know whether the infection was caused by a variant or not.