Alright let me see if I can explain it a bit, using only the knowledge I posses and from my experiences within the IT field. With that being said, you have to also realize that people call all sorts of things that they are not. For instance, a help desk or support desk (haha). Now as to how you came across these, I'm assuming you're on some site that discusses the salaries, pay grades, etc - Such as 'Indeed' or 'CareerBuilder' sites. I'd like to point out that it's not as cookie cutter as one may think. However, regardless of this all I will do the best to explain each with what I have experienced and seen personally (if others disagree, I hope they will pitch in and help me out).
1) Desktop Support This would likely be more of a entry-level position, in which you are working on End User machines. Likely to be residential though I've seen it within business side of call centers as well.
2)Helpdesk Support This is more applied to a group that supports their own product, such as a point of sale system software company will have a help desk to support the software they sell. There can be multiple tiers to this that can range from Entry Level up.
3)Technical Support This is a general term for the most part. I've seen companies like Dell use it but I've also seen hole in the wall local IT companies use it for their phone/remote support number.
4)helpdesk support analyst Honestly I've never heard of a company having 'analyst' at the end, so I cannot comment on this.
5)service desk analyst Again, analyst. If we replace Analyst with technician or support, then I have seen that as a title. With the replacement, it is very similar to the helpdesk support but I've also seen it used for a 'technical support' role in a company as well.
6)Application Support This seems a bit redundant, however this has been used for a specific branch within a 'helpdesk support' team for those who specialize in one application (sometimes the person would specialize in a few). I haven't worked along side programmers too too exclusively, so this may also be a more common term within that field.
7)System Support Engineer This is a title given to someone who's likely on a higher tier or 'level' than many/all of the above. Engineers tend to be more involved with business to business type of work, rather than repairing residential machines. This includes networks, servers, firewalls, etc.
Hope that helps some! Another good read would be the WiKi' page for 'Help Desk' which can be found HERE
PS: Once again these are from my personal experiences and are not
to be considered 100% factual definitions, though I find the replies I've given to be fair to good.