I would say the answer by @checketts is now quite out of date. Metrics are now very prominent within OpenTelemetry, with them being declared stable.
OpenTelemetry and Micrometer share some similarities in the sense that they both have metric APIs. They both have the ability to export a variety of different formats. However Micrometer is Java-specific, while OpenTelemetry has implementations in many languages. The two projects have different goals.
You can use OpenTelemetry with the Micrometer API, by using the OpenTelemetry Meter Registry for Micrometer. This will forward Micrometer’s captured metrics into an OpenTelemetry meter.