I don't quite follow your questions about "signs". Signs are physical evidence that allows identification of a disease or insect agent that potentially has damaged a tree; think beetle larvae under the bark, sapwood stain, or fungal fruiting bodies (conks). OTH, symptoms develop in a living tree, and may have multiple causes; these include a wilted crown, chlorotic leaves, or crown dieback. Some clues are a little of each, such as defoliation caused by chewing insects, unless one sees the particular critter, making this a sign.
Anyway, a lightning-struck tree would have a sign (the blown-out vertical furrow, maybe charred, which only points to lightning, baring someone lighting off a string of detonation cord), as well as symptoms over time, perhaps crown die-back due to loss of sapwood. Decay would be a new symptom; the decay organism could be identified based on signs: a virulent pathogen such as Armilaria leaves black zone lines in the wood, rhizomorphs under the bark ("shoestrings", hence the common name, shoe string fungus), and brown mushrooms at the base. See that, REMOVE IT. OTH, some heartwood decays are slow, and do not affect the live sapwood--they are saprophytes (eat dead stuff); the tree could be kept for quite a while so long as the new wood is growing vigorously. Rule of thumb: you need at least 1/3 of the cross sectional area as sound wood, but typically one would prescribe a crown thinning/reduction as an added safety measure.