Let's divide all bank accounts into savings and checking.
The main difference is that checking is easy to get money from; savings is hard to get money from. Because of this, the federal Reserve requires that banks keep more money on hand to cover transactions in checking accounts.
Here is a related question from a banking customer regarding a recent notice on their bank statement: Deposit Reclassification. It seems that the bank was moving the customer's money between hidden sub accounts to make it look like the checking account was really a savings account and thus "reduce the amount of funds we are required to keep on deposit at the Federal Reserve Bank." If they didn't have to transfer the money many times the bank could keep less cash on hand. But once they did 5 hidden transactions the rest of the money in the hidden savings account would be moved by the bank.
The 6 transaction limit is done to not allow you to treat savings like checking.
Here is a relevant quote from the Federal Reserve
Savings deposits generally have no specified maturity
period. They may be interest-bearing, with interest computed or paid
daily, weekly, quarterly, or on any other basis. The two most
significant features of savings deposits are the ‘‘reservation of
right’’ requirement and the restrictions on the number of
‘‘convenient’’ transfers or withdrawals that may be made per month (or
per statement cycle of at least four weeks) from the account. In order
to classify an account as a ‘‘savings deposit,’’ the institution must
in its account agreement with the customer reserve the right at any
time to require seven days’ advance written notice of an intended
withdrawal. In practice, this right is never exercised, but the
institution must nevertheless reserve that right in the account
agreement. In addition, for an account to be classified as a ‘‘savings
deposit,’’ the depositor may make no more than six ‘‘convenient’’
transfers or withdrawals per month from the account. ‘‘Convenient’’
transfers and withdrawals, for purposes of this limit, include
preauthorized, automatic transfers (including but not limited to
transfers from the savings deposit for overdraft protection or for
direct bill payments) and transfers and withdrawals initiated by
telephone, facsimile, or computer, and transfers made by check, debit
card, or other similar order made by the depositor and payable to
third parties. Other, less-convenient types of transfers, such as
withdrawals or transfers made in person at the bank, by mail, or by
using an ATM, do not count toward the six-per-month limit and do not
affect the account’s status as a savings account. Also, a withdrawal
request initiated by telephone does not count toward the transfer
limit when the withdrawal is disbursed via check mailed to the
Examiners should be particularly wary of a bank’s practices
for handling telephone transfers. As noted, an unlimited number of
telephone-initiated withdrawals are allowed so long as a check for
the withdrawn funds is mailed to the depositor. Otherwise, the limit
is six telephone transfers per month. The limit applies to telephonic
transfers to move savings deposit funds to another type of deposit
account and to make payments to third parties.