Yes, you are right. And even within the same bank, some parts of the bank may use VP and others AD. Banks you have to watch out for when u move have an additional executive director rank between director and MD. If u move to those banks (like UBS ) u have to negotiate for a higher rank as there is rank inflation.

For local banks, there tends to be many more ranks, so mapping is more difficult. In general, avp and below is equivalent to associate, VP is equivalent to VP or AD, and svp equivalent to director. pay for equivalent rank tends to be about 20 to 40% lower. So again, when u negotiate, be aware that u are not moving to a lower rank at the foreign house (even though u get a pay bump).