The main difference in meaning is the aspect of time. For something to accrue, it increases over time.

They both involve numbers becoming larger. But when numbers accrue they are being added to a total.

For instance the set of numbers 1, 2, 3, ... and so on is an increasing sequence but nothing "accrues". But if John owes Sue $5, the borrows $3 more without paying back anything, typically the debt accrues. Now he owes her $8. The more he borrows, the more accrues. And in this case the debt is alsi increasing.

Edit: i was wrong about borrowed amounts being considered to "accrue". Accrue is used to mean some amount that increases naturally or periodically, such as age or interest on a loan.

Increase just means to grow bigger. It has a wider range of meanings. Accrue is that too, but often has a connection with finance, and means that you receive payments over time. In accounting, it means: make provision for (a charge) at the end of a financial period for work that has been done but not yet invoiced.

Main difference: increase - very common accrue - basically only accountants & people I try not to listen to