Do words debit and credit in double-entry accounting carry any additional meaning compared to increase and decrease?

Taken from the original days of dual-column journal entries and the fundamental accounting equation (Assets = Liabilities + Equity), the definitions are just:

Debit  === left column
Credit === right column

Debits go on the left column, credit on the right. It avoids potential errors for missing a negative sign, among other things. For some account types (Assets, Expenses), a debit is an increase to its normal value, for others (Liabilities, Equity, Income), it's a decrease.

DEALER is one mnemonic that is used to help remember which is which:

Normal Debit:
               Dividends
               Expenses
               Assets
Normal Credit:
               Liabilities
               Equity
               Revenue

Although I typically found it easier to just think in terms of the fundamental accounting equation (A=L+E) and work out Expenses and Revenue logically from there.

If you can better understand things in terms of increases and decreases for different account types you'll probably be fine, but you'll no doubt work with people that have internalized "debit" and "credit" and use those terms without having to translate to increases and decreases.