is mysql 5 able to manage transactions between different users ?

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hi !
in mysql doc it is stated that :
"MySQL supports local transactions (within a given client connection) "
ref :
but what happens if for instance 2 different users tries to modify same
data in 2 different transactions in 2 different connections ?
does the last one which finish simply "win" (erasing the other's work)
or does mysql is able to lock rows in a correct way via transaction
managed locks like oracle/postgrsql/sqlserver/etc. between users' sessions ?
thx & regards,

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