What is the difference if we use Decision Tree as Base estimator in AdaBoost algorithm ?
Is Random Forest a special case of AdaBoost?
Most certainly not; Random Forest is a case of bagging ensemble algorithm (short for bootstrap aggregating), which is different from boosting - check here for their differences.
What is the difference if we use Decision Tree as Base estimator in AdaBoost algorithm ?
You don't get a Random Forest, but a Gradient Tree Boosting Machine, available in several packages like xgboost (R/Python), gbm (R), scikit-learn (Python) etc.
Check chapter 8 of the excellent (and freely available) book An Introduction to Statistical Learning for more, or The Elements of Statistical Learning (heavy in math & theory, not for the faint-hearted)...