Merging in git and in hg works the same, opposing to the believe I had over the last 5 years.
In git, you check out the branch you want to merge into. Then you execute git merge <branch>, where <branch>, is the branch you want to merge into the current branch.
In hg (particularly TortoiseHg Workbench), you update to the branch you want to merge into, then select "Merge with Local…" on the commit you want to merge into the current branch.