I would lean towards (but I'm not 100% there) having four tags, two for wood (wood-repair wood-maintenance) and two for tools tool-repair (tool-maintenance).
wood-repair: Used for questions like your first example "How can I repair a split in a board"
wood-maintenance: long term care of a finished product. Probably replacing the dumb long-term-care tag that I created. Used for questions about how often they should refinish something, should it not be placed in sunlight, etc.
tool-repair: Fixing broken equipment
tool-maintenance: Maintaining equipment in good working order. Oiling, sharpening, aligning, storing, etc.
It's possible this is too fine-grained but this is the first solution that came to mind and at least it puts every concept in a nice spot. On the other hand, wood-maintenance is not a term someone would think of when wondering about how to care for their finished product. There's probably a better name for this.