Amusingly enough, it seems like by swapping the kanji in 始終 you can get a slightly different word. What is the difference between the two of them? I found some answers on Japanese sites but reading them I feel like I'm just going through a bunch of synonyms and very similar descriptions. An English answer would really help...
始終（しじゅう） is relatively rare in modern Japanese, except that a four-kanji compound 一部始終 is common. Standalone 始終 mainly appears in stiff literary works as an adverb meaning "all the time". If I heard 始終 in conversation, I might not understand it.
終始（しゅうし） is much more common than 始終. It can also mean "all the time" or "always", but I think it tends to mean "from beginning to end (of a certain event, etc)" more often. 終始 is also a suru-verb. ～に終始する is a common phrase meaning "to do only ～ from beginning to end."
The meeting was in a good mood from beginning to end.
In his speech, he entirely focused on making excuses.