With the caveat that I'm not an expert - I think not quite.
I've always thought that a barrister was a specialist legally qualified person that represents people in court either for the prosecution or defence.
Whereas lawyer is, I think, is anyone legally qualified to give legal advice - so a barrister would be a lawyer but so would a solicitor.
I've kind of seen the term lawyer as like term Dr is in medicine - a term for anyone qualified to practice.
Whereas barrister would be more like cardiologist or pediatrician. A specialist lawyer that works in court