When a poem falls into the grey areas of categories 2 or 3, and if one insists on categorizing such poems (one may choose not to), then one has to exercise discretion based on the tone or mood of the poem. I tend to think that if a poem is serious, then it is more likely haiku (that is, poems in categories 1 and 2 would be haiku, more likely). Some people think that if a poem is humourous, even if about nature, that it is a senryu, but here I would disagree. I think poems in category 3 also tend to be haiku rather than senryu.
Of course, final judgment of a poem, if one insists upon it, depends on the poem itself, but I tend to find that most poems in categories 1, 2, and 3 are haiku, although categories 2 and 3 do lean on some aspects of senryu. It may be more accurate to say that all four categories are “haiku,” and that “senryu” is simply a subset of haiku.
Some people take issue with this latter claim, however, and make very sharp distinctions between haiku and senryu—and I understand that this is particularly the case in Japan, where haiku and senryu are much more vigorously defined and segregated. In the English language, my feeling is that too much emphasis can be placed on making the distinction—to the detriment of pure enjoyment of good poetry. So long as one has one’s priorities set, an exploration of the distinctions can prove interesting, especially if it helps one improve the quality of one’s poetry.
Another way to explain the relationship is that haiku and senryu are “cousins”: they are not too distantly related, but do have the same grandparents. In other words, some “facial” features are similar, but they are not as closely related as brothers or sisters.
At the very least, I think humour is underappreciated in both haiku and senryu, as are satire and irony—all good techniques that, if handled skillfully, without veering off into poetry that is merely superficial joking, can make for lively poetry.