It is both and neither.
The simple mechanics: If a bond yields 5%, and interest rates go up to 6%, the 5% bond price will go down. Yield up, price down. The extreme situation would be massive inflation. Bond pays 5%, interest rates go up to 10%. The 5% bond is now worth significantly less than it was when interest rates were 5%.
Bond funds are short, medium, long term or combo. If the short term rates change (overnight) that will affect the short term prices much more than the long term, as the rises and falls in interest rates do not match each other.
Your fund will constantly be buying and selling bonds. They will buy some at the new price and you will get some of the benefit. But they will lose principal when the sell the lower interest rate bonds, so you lose. Most people don't buy bond funds for capital appreciation, but income. I have a couple that I have owned for years. They are "underwater", or trading at a price below what I paid. Nonetheless, the return on investment ( interest dividends) has been enough over the years to make them very nice investments that I intend to hold onto.
Bond funds tend to be stable, we are just at the tail end of massive decades long bond boom. We probably won't see significant upward movement in bond funds for some time. However, if you are happy with the yield, who cares? The real danger is quick inflation, which is a bond killer.