In the US (and perhaps in other countries too), the closest approximation to
"An investment plan which gives daily profit, where the funds (initial investment plus profits) can be redeemed at any time"
is an ordinary bank account (checking, savings, etc) or a money market fund account. Both entities credit interest earned (which the OP calls profit) to the account on a monthly basis, but the interest accrues on a daily basis, so that if the account owner closes the account in the middle of the month, the account owner gets the entire sum invested as of that date (including interest accrued but not as yet credited to the account as of that date). What if the account owner doesn't close the account but merely withdraws some of the money, say $100. Does that $100 include the interest accrued but not credited as of the date of withdrawal, or is it purely the "original" investment that has been withdrawn and the interest accrued thus far stays in the account and has not been withdrawn at all? Inquiring minds want to know the OP's take on the matter.
With regard to
"An investment plan which gives profit for a specific time period, where the funds (initial investment plus profits) can be redeemed only at the end of that time period"
the closest equivalent in the US is Certificate of Deposit (CD) which pays interest at a fixed rate and can be redeemed only at the end of the specific time period when the original investment plus all the interest is paid out. Most CDs can be "broken" in the middle of the specified time period, but this action comes with various drawbacks such as interest might be paid at a lower rate than the one agreed upon for the time that the money was invested, and/or a fixed penalty for "breaking" the CD prematurely. Either way, one gets a reduced profit, or maybe even suffers a loss, depending on the exact terms governing the CD.
It is worth noting that banks in some countries don't have CDs (where the interest is credited to the CD monthly or quarterly and adds to the redemption value of the CD) but have Fixed Deposits where the interest is paid out monthly or quarterly into a linked checking or savings account.