When you buy a bond, does the interest rate stay the same over time as when you bought it?

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I heard on TV how back in the 80s, bank accounts, money market accounts, CDs, bonds, etc., had really super high interest rates, 10% being the norm & some even 12 or 14%. I was wondering, when you buy a bond, & it's a certain interest rate, does that rate stay the same the whole time, or does it go up and down with the market? Like in other words, say you had bought a bond back in 1988 or something, and the interest rate was 10% at the time and you decided to let it sit til now to cash it. When you went to cash it, would that mean you'd get the 10% when you went to cash it? Even though the interest rates have dropped? And vice versa, if you bought a bond today that had a much lower interest rate, but things got better, would you possibly gain more interest on it in time? Or do bonds stay exactly the same the whole time. I hope this makes sense how I'm wording this.

When you buy a bond, does the interest rate stay the same over time as when you bought it?