Using HTTP status codes in your responses is a trap. It conflates the API transport with the actual semantics of the API. The goal of HTTP error responses is to say that something went wrong in the transport layer. The goal of API error responses is to say that something went wrong in your service. For example, your HTTP REST server may be perfectly fine, but your back end DB may be misbehaving. Having separate API level error responses, for example an explicit field called "error" in your JSON response, I consider to be best practice. Frequently your client needs to know the difference, for example to determine what kind of error to return to the user or what retry strategy to use.

In typical HTTP REST services this transport/API error split makes it really easy to create client code which only needs to check two conditions - if the HTTP response code is 200 or not, and if the error value is set or not. You also don't have to shoehorn your error handling into the very limited set of errors provided by the HTTP protocol.

The other real-world advantage of this is that when you outgrow HTTP as the transport protocol for performance reasons this makes porting the API really easy to, e.g. protobuf RPC, or even raw TCP. The error is already defined as part of the API and you don't need to rewrite all your client code to deal with mapping multiple HTTP response codes to your new transport. It's good future proofing I've seen pay off in a at least a couple of real-world cases.

Bottom line - your server should always return HTTP status 200 and a separate API error response.

There's also a reasonable debate to have about whether non-error responses should also include an explicit "error" field with some default OK value. There may be good reasons to leave it out, e.g. if you want to save bandwidth, but I consider that a fairly insignificant point. For consistency my APIs always return a default OK error field on non-error responses - your mileage may vary.