Wood fires do not need air directed from below to burn successfully. In fact they ‘prefer’ to sit on a bed of ash which helps slow the rate of burn and give maximum efficiency. Hence, woodburning stoves tend to have just a flat base on which to build your fire. Some woodburners have a grate and even an ashpan, but the idea is that you don’t clean out the stove every day - you light each new fire on the ashes of the previous one. Once every week or so (depending on how often you use the stove), you can either shovel the ashes out, or, knock them out into the ashpan if provided, and then start again.
A multifuel stove will have a grate of some description, with or without a riddling mechanism. Solid fuel (smokeless ovoids or anthracite) will burn best if air is directed into the fire from below. The grate needs to be kept clear and must not be allowed to get too clogged up with ash as this restricts the burn of the fuel. In other words, if you burn solid smokeless fuel you will need to knock, (or riddle if possible) the ashes into the ashpan, and empty it every day.