Thanks for this important questions, because every one should know this –
I can say from my own experience that, all these accounts are financial accounts having differences among them. I’m trying to say in details:

Current Account 
Current Accounts are generally for used for business purpose and allow a large number of transactions, multiple cheque leaves and a host of other free services. However, these accounts are typically low yielding I.e. Banks pay nil to very low interests on these accounts. In Current account, the transactions are done frequently. The number of free transactions are maximum in this type of account.

Savings Account
Savings Account generally one’s savings are kept. these are accounts used for savings and are generally opened in individual names. Banks provide better interest rates in savings account when compared to current account. The number of free transactions and free cheque leaves on offer are lesser than current accounts (this may vary with each bank and variant of saving account opened in each bank). But Savings Account are not the ones which hold maximum interest rates for customers. You can say it is in the middle tier. Free transactions are relatively less when compared to current account. However, interest rates may vary upto 6% especially in India.

Deposits Account
Deposits Account is the long accounts wherein a customer commits to a fixed amount to be kept for a certain period, ranging from as low as 3 months to 15-20 years. Basis the duration/ tenor, the rate of interest may vary. Withdrawals are not allowed in the contract period. In case a customer wants to break the contract and withdraw money from such accounts, banks may levy penal charges, reduction in interest rates etc.

These accounts accounts are verious  types but in most of the bank we notice  2 types of Deposits Account:
Fixed deposit
Fixed deposits are also commonly known as term deposits. In such type of accounts, customers deposit a fixed amount of money for a fixed period (3 months to 15 years) at a fixed rate of interest. In this type of FD investment banks provide maximum interest rates. The principle amount is deposited in an account and interest is added to it for a fixed tenure. There are no withdrawals or deposits allowed in the middle of the tenor.

Recurring Deposit
Recurring Deposit accounts also fall in term deposits catergory. as in case of fixed deposits, customers commit a fixed amount of money for a fixed period at a fixed rate of interest. The interest is provided by the bank at the end of this time period. However, in this case the money to be deposited is done on fixed intervals (generally monthly basis). Thus, one may deposit a fixed amount of money every month. Owing to recurring nature of the deposit, the account gets its name. No interim withdrawals are allowed. This account is suitable for those who do not have a sum of money to be deposited but have a regular flow of income. 

Capital Account
Capital Account  accounts hold details of a government or a country’s financial statements. All the national level transactions are handled through this type of account. It holds the balance of payment of a country. This account includes foreign direct investments (FDI) and other national level investments.

Hope that the above points help you understand the differences among the various accounts mentioned.

Thanks.