Ignorability, unconfoundedness, and satisfaction of the backdoor criterion mean the same thing. They all refer to there being a set of variables (possibly empty) that when conditioned on (i.e., stratified upon), the causal effect of the treatment on the outcome is nonparametrically identified as the association between them. You can think of it as all confounders being measured (i.e., no "omitted" variables), but it is a little more complicated than that, because it also involves not conditioning on the wrong variables (e.g., colliders). Satisfaction of the backdoor criterion is sufficient for nonparametric identification of the treatment effect.
The front door criterion is another condition for which satisfaction is sufficient for nonparametric identification of the treatment effect. It is almost never used because the condition is almost impossible to satisfy in real data. I encourage you not to focus on the front door criterion as you educate yourself about causal inference. It is a niche topic that serves solely to illustrate the power of causal graphs to illuminate theoretical ways to compute causal effects, but not one that is used in practice. It has little to do with ignorability or unconfoundedness.