It is possible for data to be altered in a way that leads to no change in the checksum.
Two files, network packets, etc. can have the same checksum.
Checksums are usually much simpler and faster to calculate than hashes. They are simple enough to be used for high-speed
applications such as network protocols, e.g. the Frame Check Sequence in Ethernet.
Simple checksums are not sensitive to the order of the input data; the kind which is mostly used is a cyclic redundancy checksum
(CRC) which takes into account the order of data.
Common checksum algorithms are designed to be implemented in hardware, so that they can be embedded in network devices for
example. They are also designed to detect the types of errors that commonly occur in transmission of data (small groups of errors
close together, called burst errors).
You will sometimes see the term "checksum" used to mean both hashes and the simpler type; be sure you are clear what is meant.