Earlier quoted context omitted.
I have never used Fossil, but I used to be a strong proponent of Mercurial. My advice is don't - Mercurial lost, git has won, and fighting against the current is just going to make your life harder. The main advantage Mercurial has over git is a command line syntax that makes consistent sense. The operations you want to do are easy and as you try and do more complicated things, the new commands will be unsurprising a…
I know Git inside and out, but I had to use Mercurial for a client a couple years ago. I found it to be the most baffling and nonsensical source control experience of my life. It might be a case of cross-contamination. Like you said, each SCM uses similar terms for different concepts, so my Git knowledge may have unfairly colored how I expected similar terms to work in Mercurial. But stuff like: "hg log" gives you _e…
The 'original' branching method for Mercurial is called Named Branches. The big difference with Git is that every commit is labelled with what branch it is on. This has advantages - if you imagine looking at the train track of 'master' in git with it's divergence for a few commits and then merge, you can see that the 3 commits were on a branch called 'performance', whereas with git that history is completely lost. See: https://www.mercurial-scm.org/wiki/NamedBranches
As usage of git grew, the git branching model gained popularity and so the Mercurial bookmarks extension was created (https://www.mercurial-scm.org/wiki/Bookmarks).
It can be seen as a downside that there are two branching options that you have to choose between.