Is the difficulty setting for the campaign map only, or also battle difficulty?

[Dr. Livesey]

When you start a game there is a difficulty slider. Does this only effect the diplomacy, economy, and other factors in the map screen... or... does it also change how hard actual battles are?

I'm hoping it's not for the actual fighting. I want that to be the hardest available, but I do want some grace in terms of economy and other stuff that goes on in the map page.

[rory.b.p]

Everything, on harder difficulties enemy units get buffs in stats in battle, you suffer hidden diplo penalties (basically everyone wants you dead) and the AI also gets massive buffs to their economy allowing them to field multiple full stacks even if they are down to like 1 province.

There are various things which can alleviate this problem on higher difficulties but they are double edged swords.
For example in a VH or Legendary campaign you can sell millitary access to your ares to neighbours for a quite large sums of money, but unlike lower difficulties where the AI will pay you a little less but if you do this on Higher Difficulties it almost guarantees the AI will march an army right up to your city using millitary access then declare on you.

I think you said you were playign an otomo campaing, there is a super high risk strat you can use that gives you a serious fighting chance vs the AI economy on VH or Legendary.
Take you Daimyo with an army ASAP, through him on a boat and send him somewhere nearby but an area that you never plan on using or holding.
Capture one of these throw away provinces and loot it for max cash, then build rental land (can't remember what its called but basically you get a few thousand Koku but the land slot gets locked), rinse and repeat in for 5 or so turns (by now you will easily have 40-50,000 Koku in the bank and you will have been using this to build your armies back on Kyushu).
By now due to the land lease and the looting your daimyo will be incredibly dishonourable so send him into a battle he can't win and have him die..... (this will wipe away his dishonour because well he is dead).
Its risky because there will be a short period of time where you will be weak at home but if you can survive this 1-2 turn period then you will be able to expand rapidly and take Kyushu.
Then get some Nanban trade ships send 1 to each trade node on the map and use 3 to lock down Kyushu from enemy naval invasion and you have essentially bought yourself an easy start to a VH or Legendary Otomo Campaign with Kyushu lockdown and a bunch of rebel provinces the AI can't use in a random area of the map with 1 land slot lockdown in lend lease.

[easytarget]

I set the difficulty the same so I'm not certain of the impact of this setting, but I have noticed that when you start a campaign there's a difficulty setting for the campaign as a whole, and then once you dive into a campaign if you bring up the game settings menu inside the campaign there's a setting for battle difficulty.