The difference is more apparent when discussing ideas. A frequentist will not assign probability to an idea,idea; either it is true or false and it cannot be true 6 times out of 10.
An event1 with Bayesian probability of .6 (or 60%) should be interpreted as stating "With confidence 60%, this event contains the true outcome", whereas a frequentist interpretation would view it as stating "Over 100 trials, we should observe event X approximately 60 times."