Do passenger missions count as "Trade"?

Some missions count towards exploration rank (collect data and sightseeing adventures), some count towards trade rank (seeking transport).

When taking a passenger mission, you can see what is the recommended rank - if it is a trader rank (e.g. mostly penniless), then it will count towards trade rank, if it is an explorer rank (e.g. mostly aimless), then it will count towards exploration rank.

As mentioned in the answer by @Gedas, only "Transport" type passenger missions will contribute to your Trade rank.

Unfortunately, passenger missions do not count towards your "profits from trade" statistic in the Status panel, nor do they count towards any Powerplay benefits concerning trade vouchers, such as the Rank 2 benefit from Edmund Mahon.