Maybe u/ParallelPain has some more detailed info on this.

However, generally speaking:

I should note that I am referring to taxation of land: the taxation of urban populations, i.e., merchants, by necessity, had to function differently (and I actually do not know how that worked).

There is something called the agrarian myth of the traditional, rice-producing Japanese farming society.

If you take a look at earlier medieval documents, such as the records of goods submitted by the inhabitants of estates, the products submitted are actually all over the place: ores, metalworks, silk, lumber, fish, salt, various fruit, grains, etc.

However (probably facilitated with the emergence of the stipend, as opposed to direct ownership of landed property by individual samurai) this situation leads to one problem: it is difficult to compare the relative value of things without a common unit of measurement. The unit of rice (and its associated value measured in quantity by koku) eventually served as the “currency” in administrative documents utilized to comparng the relative productive power of land in the Edo period, even if that land did not actually produce rice. (on Sengoku-era management of land, I am betting on PP)

Hence, it is historian Amino Yoshihiko’s - who spent more or less his entire life arguing against the above-mentioned myth - argument, that, at some point in the administrative record, rice was used in such calculations, even if the people paying tax didn’t actually pay in rice. This makes perfect sense: how should a coastal settlement subsiding on fishing and salt fields, with no terrain suitable to cultivate rice in the first place, suddenly start producing rice?

This means that, at least for rural society, you end up with an overrepresentation of rice in any cursory survey of agrarian production, because the records simply calculate the value (which determines taxation and so on) of an area as measured in rice, no matter what the people dwelling there actually did.

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(see Amino's Rethinking Japanese History for an overview of his argument)

While the predominate tax, at least recorded, was on rice, there were definitely taxes for the mines. The famous Iwami Silver Mines is recorded to have paid approximately 600 kg of silver in taxes to their Mōri overlords in 1581. During the Edo era the bakufu directly appointed men to oversee the major mines like Sado and Iwami, and in its recorded that in 1602 the mines sent to the Bakufu about 37.5 and 15~19 metric tonnes of silver respectively, so you could almost think of them as state-run enterprises, and the metals were used to make coinage. Considering the gold of Kai were also used to make coins (or at least stamped pieces), it might have been effectively "clan-run" as well.

For farming taxes, at least in the Edo period when records are clear there were definitely taxes on other produce, at least on areas that predominately grow other things, though given some example records of how farms were run, if you grew rice your burden was probably calculated on rice alone even if you grew other things at the same time. As /u/Morricane said, at the macro level (domain/province level), it seems in the Edo period this was calculated to its equivalent in rice and then combined with the actual rice tax in the calculation.

Taxes paid by merchants and artisans, as well as hunters, fishers, etc were called unjō or myoga, they seem to be paid more like a rent (or land-usage-fee) than an income-based tax. The practical difference between the two also doesn't seem to be very clear. Both were paid in kind or in currency, probably agreed-upon with the lords. Like the saltpeter tax on the Gokayama villages, these seemed to have been calculated based on the needs and wants of the government, rather than a set percent of what was produced. Also, these and the mines didn't seem to have been restated into koku. Or perhaps they were purposely excluded in documents the domains gave the bakufu as part of an attempt (like submitting outdated documents) in order to try to lower their tax burden, which the bakufu most certainly knew but turned a blind-eye on.

One more very important tax that is often overlooked is the tax on time and labour. The general population were often mobilized to work on dykes and irrigation, as porters, or to staff post stations and deliver messages. They were often poorly paid for these, and sometimes not at all. And one didn't have a choice not to get mobilized for these duties, though from the high-Edo onwards people started to pay their way out of these, which presumably the government would use to hire labourers for the task. Likewise, the tax on the samurai were basically more of a levy for labour. This is especially true for the landed samurai (including the domain lords) as their land were guaranteed by the government, but they needed to put in the time and resources to do the government's bidding when called upon. In the Sengoku this was usually in the form of troops during war (a type of levy/conscription). In the Edo era meaning usually living in Edo and help run the government (sankin kōtai), with any incurred expenses again often out of their own pocket. Tokugawa Yoshimune tried to implement a 1% tax by koku for all domains in return for halving the duration the lords were required to stay in Edo, but it caused a huge amount of problems and was quickly abolished.

EDIT: Also note that for most the the Sengoku, most places were using the kandaka system. Under this system a piece of land was expressed by the amount of tax revenue, in currency (or kanbun), one can extract from the land. The later kokudaka system expressed the land in the total rice produced from it, from which the lord was then to take a certain portion.