I guess, to answer the question of 'what's going on?' I could simply say that the differing dates reflects a couple of the complexities of the "Vietnam War". So, even calling it the "Vietnam War" plays into that, it presumes to take the American involvement in Vietnam angle on what in reality was a decades long effort of Vietnamese independence and civil war between factions and governments. That's why it is often referred to the "Second Indochina War", as opposed to the First and Third (French in the first instance, Cambodian, Vietnamese and Chinese in the case of the third).

But to answer your question, in relation to the Second Indochina War (or the "Vietnam War", or the "American War" if you ask some Vietnamese), the reason there are a few dates here is fairly simple. For instance, there was no official 'declaration of war' by the US on North Vietnam, nor on the insurgency threatening their allies in South Vietnam. However, the Gulf of Tonkin Resolution of 1964 - to me - does signal a change in what was a gradually escalating situation from the late 1950's and early 1960's. I would be tempted to say, personally, that is when America started to 'properly' go to war in Vietnam... So if we were taking that primarily American perspective and saying 'when did America go to war?' You could throw that date out fairly confidently in my books.

That being said, by this point many of the things that we associated with the so called "Vietnam War" were already happening. Defoliants such as Agent Orange had been sprayed from planes as early as 1961, Americans had already been killed in combat or in NLF attacks, the insurgency of the NLF had already taken huge amounts of territory into their effective control by 1962.

As for the other dates given, they can also be reasonably pointed toward as 'starting points' of a war that had really already been going for more than almost two decades. In 1959 the North Vietnamese Politburo decided to support armed struggle in the South. In 1955 Ngo Dinh Diem has kind of, consolidated power in the South and declared the Republic of Vietnam (usually just termed South Vietnam). So if we took that date as an example, and that one out of the list you gave is probably the least relevant, you could argue that the establishment of the Republic of Vietnam, Diem as leader, US state building... all of those are in play and characterise one of the belligerents in the so called "Vietnam War". The other date, 1954, to me that signifies Geneva more than anything else, the partition, the 'reset' after the war with the French... and things gradually escalate from there, so it isn't wrong either. None of them are.

But the point is that "the Vietnam War" is really just the resumption of a much longer war, not just with the French but reflecting a larger Vietnamese civil war. That's why the dates are a little all over the place and subject to change depending on what the historians are trying to say.

Vietnam isn't exactly my area of expertise so some others may want to weigh in and expand or correct me but that is the general reason why you've got a couple of dates to work with.