SIMMERING generally means to cook just at or below the boiling point. When it makes a significant difference, you will be instructed as to the precise level required for any given recipe. For instance, we can simmer at a slow boil, just barely at the boiling point or just below the boiling point.
If we need to redefine these points further, you will be instructed to simmer at the breaking or rupture point (at that point when the bubble becomes just large enough to break–which is more like a hiccup than a boil–usually occurring in thick sauces); or just below the breaking or rupture point (when the bubble rises up from the sauce, but instead of rupturing, it subsides, and then rises again).
Simmering at the fizzle point refers to lots of tiny boiling bubbles in the liquid, giving the appearance of carbonation.
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