No. Angina can show up several ways, and some of them don't feel like "heart" at all.
Classic markers: pressure, tightness or heaviness in the chest, brought on by exertion, cold, a heavy meal or stress, easing within minutes of rest. Pain may spread to the left arm, both arms, jaw, neck, throat, upper back or between the shoulder blades.
Less obvious markers, especially in diabetics, women and older people: breathlessness on effort that seems out of proportion, unusual fatigue with activity, nausea, sweating, light-headedness, a sense of indigestion or burning, or pain only in the jaw, teeth, throat or arm with nothing in the chest. Some people have no pain at all and just notice they've unconsciously slowed down over the years because activity feels wrong.
What makes it angina isn't the location or the sensation; it's the pattern. Predictable trigger, predictable threshold, resolves with rest. That's what you described.
Two other things worth knowing. Pain that comes with a specific movement or posture, or that you can reproduce by pressing on the spot, is usually not angina. And pain that appears at rest or wakes you up, or that's getting worse over weeks, is unstable angina and needs emergency assessment, not an appointment.
Does pressing on the spot with your fingers, as in the photo, actually reproduce the pain?