Arrhythmia. Tachycardia is a general term applied to any fast heart rate including tachyarrhythmias. A tachyarrhythmia specifically implies a form of arrhythmia which causes a fast heart rate, not all arrhythmias cause a fast heart rate. Tachycardia is defined as a heart rate more than 100, normal heart rhythm is frequently more than 100 in exercise, excitement, fevers, etc. None of these are arrhythmias.
Regular vs Abnormal. Both mean rapid heart rate but tachycardia usually refers to the normal rhythm just beating faster than normal (sinus tachycardia). Tachyarrhythmia usually refers to an abnormal and fast heart rhythm such as atrial fibrillation, atrial flutter, supra ventricular tachycardia (SVT) or ventricular tachycardia (VT).
Tachycardia. Very similar terms. You can have sinus tachycardia which is the term for healthy speeding of the heart in response to things like exercise, excitement etc. But tachyarrhythmia refers to having an abnormal fast heart rhythm and there are several types of it.