When discussing accrued interest vs. capitalized interest, we’re, in fact, talking about very subtle differences in meaning that mostly concern the speaker’s viewpoint and the context.
Both types of interest are accrued - that is to say, accumulated - and both are added to the principal, increasing both the principal and the interest that has to be paid on it in the future.
However, we mostly talk about accrued interest in the context of savings accounts, while capitalized interest is something you’ll come across when reading about loans and what increases your total loan balance.
For companies, the difference between the two concerns the way the interest is recognized in accounting - as an interest expense in the current period (accrued interest) or as part of the loan balance (capitalized interest).