It's not as simple as being "more of a trade." It's quite similar to the distinction between physics and, say, aerospace engineering in that regard. I'd never describe the latter as being a vocation or trade.
Agreed. Engineering is a "profession". You wouldn't call medicine or law "trades". In some jurisdictions (Canada for example) calling yourself a "software engineer" without having a professional engineering license is unlawful (although lots of people still do it and it's difficult for the regulatory agencies to enforce it at scale).