This is a very complicated thing to explain on this forum, I think you would be better off googleing blood pressure and reading about it. Blood pressure and heart rate usually work together but are independant systems. The Heart can beat faster to increase blood flow, it can also beat harder instead, or as well as. Blood pressure is controlled by how constricted the arteries are. This is controlled by other organs in the body. So, if the arteries are tightly constricted, blood pressure will be high, but the heart could be pumping slowly. The arteries can be fully dilated, reducing blood pressure but the heart can beat fast but not really increasing pressure. It really would take a lot of room to explain it all.
sorry, I meant to add, conditions and activities affecting heart rate/blood pressure will greatly differ between individuals. Some people running will have very high blood pressure and a high heart rate. Some will have normal blood pressure and high heart rate. Some will have normal heart rate and lower blood pressure. Our bodies are not all the same and a lot of it has to do with fitness.
If I do star jumps, it takes around 30 seconds for my heart to reach 100bpm. It takes my 15 year old sons 5 seconds. After 5 mins, my heart is at 140. My sons is at 100 after 15 mins. My blood pressure goes up to 160/85 his goes up to 125/70. So I assume age is another huge factor. He is panting a lot more than me and very red in the face, whereas after 15 mins Im not having much trouble. If however I try to walk up an incline of any degree, my pulse reaches 160 and my bp goes up to 180/95. Im also struggling for air. His is 102 and bp is 120/70.