There are two ways to write Shinsengumi in Kanji…
The first and what most of us know is…
新選組
and the second…
新撰組
The difference is the middle Kanji. In the first sample the kanji 選 is truly pronounced as “SEN”, while the other is “ERABU”. While both of them practically have the same meaning one is to “select”, the other is to “compile”, apparently what was used in the Shinsengumi was varied amongst the corpsmen. The first kanji above was also seen as what Kondou used in his letters to Tama in My 1864. The second sample was seen in the Aizu documents that referred to the Shinsengumi. Since both kanji virually mean the same, there’s really no big deal in the difference IMHO But most of us use the first sample too.