The distinction is given by the publisher themselves (not a fan thing), so I think the 3 terms have their place here.
I see it like this more or less:
- Series: low budget, ~25min, ~13+ episodes, for TV/general public. (
ex: 13 eps)
- OVA/OAV: medium budget, ~30m-1h, 3~6 eps (sometimes 1 full movie but less common), tipically direct-to-video (may include riskier stuff). (
ex: 4 eps)
- Movie/film: high budget, +1:30h, usually theatrical release/general public. (
ex: 1)
I don't think how they are broadcasted matters really, just the publisher's intention. Some examples.
- studio makes a series, nobody wants to broadcast it on TV, they sell it via DVD or put it on the web > still "series" (IIRC this has happened in Japan).
- In the US most TV series are sold direct-to-video/DVD > still "series".
- A few OVAs are published, later a TV broadcasts them > still "OVAs".
- Some products have both standalone (1 ep) OVAs and movie releases labelled as such,
ex.