They are synonyms for each other and can be used interchangeably.
In .Net, there is a class called SqlConnectionStringBuilder that is very useful for dealing with SQL Server connection strings using type-safe properties to build up parts of the string. This class keeps an internal list of synonyms so it can map from one value to another:
+----------------------+-------------------------+
| Value | Synonym |
+----------------------+-------------------------+
| app | application name |
| async | asynchronous processing |
| extended properties | attachdbfilename |
| initial file name | attachdbfilename |
| connection timeout | connect timeout |
| timeout | connect timeout |
| language | current language |
| addr | data source |
| address | data source |
| network address | data source |
| server | data source |
| database | initial catalog |
| trusted_connection | integrated security |
| connection lifetime | load balance timeout |
| net | network library |
| network | network library |
| pwd | password |
| persistsecurityinfo | persist security info |
| uid | user id |
| user | user id |
| wsid | workstation id |
+----------------------+-------------------------+
(Compiled with help from Reflector)
There are other similar classes for dealing with ODBC and OleDb connection strings, but unfortunately nothing for other database vendors - I would assume the onus is on a vendor's library to provide such an implementation.