I am a new learner of Iwasawa theory and currently reading the famous paper by Skinner-Urban in 2014, and the following-up works by many other people. When reading these papers, I found that some people tend to work over the general symplectic group $\mathrm{GSp}_{2n}$ and general unitary group $\mathrm{GU}_{r,s}$ (i.e. the ones with similitude factor) rather than the groups $\mathrm{Sp}_{2n}$ and $\mathrm{U}_{r,s}$ without similitudes. Yet meanwhile, some people often work with the ones without similitude, especially when doing quite explicit calculations (e.g. the pullback formula in Skinner-Urban's paper). Still, at least from the perspective of readers as naive and stupid as me, some authors just "randomly" switch the groups they are working with, without any hint.

So I wonder that what are the essential differences between the ones with similitude and those without similitudes? Why do people prefer one over the other?

I am so sorry if this post does not fit this advanced site and thank you all for commenting and answering!