It does seem that these days each email account server (yahoo, gmail, outlook etc) and clients (outlook program, thunderbird, mail etc) all have their own versions / takes on filtering spam.
What does the online server webpage of the mail account show? That is the definitive of whats in each mail folder, and clients and programs should sync from that base account.
If all the spam is there in the inbox, then its down to the clients that are doing the filtering. Programs like outlook seem to guess at what is spam and automatically take it out of the inbox and put it into a spam folder. When they do that, then that should also sync that filtering back to the server side so that the spam on the server also gets moved out of the inbox. … so in theory other programs that sync to the mail server dont see the spam in the inbox anymore either.
Perhaps its simply the case that the desktop client is better at doing this filtering than the ipad, but that the desktop isn’t getting to do its filtering before the ipad looks at the server (imagine only using the desktop once a day, but the ipad every hour – the ipad wont see a filtered inbox till the desktop syncs later on )
AS I say, i’d be looking at all 3 (web, client, ipad) and comparing.