Woolf tells us in the introduction to the 1928 eidtion of her book that Septimus is intended to be the double of Mrs. Dalloway. Indeed, she first thought that he might live while Clarissa would die. As a result, many critics understand his death to be a substitute for Clarissa, for if he dies for his war experience (especially the death of his friend) and his inablility to adjust to life, she is able to live, to adjust to the confinements of her married life. Clarissa's meditation on Septimus's death at her party indicates this intuitive closeness she feels to a man she has never known. "Death was defiance," she tells herself. "Death was an attempt to communicate. . . . Had he plunged holding his treasure?" "What a plunge" begins Mrs.Dalloway, and the treasure she holds was her moment when Sally Seton kissed her. Septimus shared a similar close relationship with his friend who died at the front. Clarissa also says at her party, "She felt somehow very lke him....she felt glad that he had done it; thrown it away. . . . He made her feel the beauty."
I believe Septimus and Clarissa both start from the same point. They couldn't accept their reality for what it is. But they are, however, differentiated by their choices. Clarissa moves in her life by choosing a safe option while sacrificing her love to Peter. Also, she is always keeping herself busy with parties and such things just to escape from the reality. On the other hand, we have the one who tries to face the reality and thinks, for a brief time, that he really did. However, it turns out that his experience in the war takes from him more than what it gives, if any. When he faces the horrible realty that Clarissa keeps escaping from, he has lost his mind!
The similarities are that both Septimus and Clarissa feel that they are outside floating in the world, looking on at themselves at the world ahead of them and their actions but at the same time dashing headlong throughout the passage of time. They feel very lonely and also very isolated from the world and feel very uneasy about themselves.
But they do differ from each other. Septimus went to war and tried to defend his country from being attacked and attempted to become a "man"" but unsuccessfully lost the war. At the other hand, Clarissa, did not fight in the war. she married a safe man who would not dared her to become more of a woman that she believed herself capable to do it, but she was wrong.
They both couldn't adjust to the world like it was, full of minor worries and major prejudices.
They are both very isolated and feel alone. They're also not comfortable in their situations and at odds with the world at large.