The main difference between patience and perseverance is that patience is the ability to endure difficult situations without being annoyed or anxious, but perseverance is the quality of continuing with something even though it is difficult.
Basically, patience and perseverance are two virtues everyone should aspire to cultivate in life. A patient person is calm in the face of provocation, annoyance, delay misfortune, or pain, and does not lose temper or become irritated or frustrated. Perseverance is simply not giving up, however difficult a task is.
The martial arts path cultivates both.