What is the difference between NFC Forum Tag 2 and NFC Forum Tag 4 standards? Are they inter-compatible in any ways?
There are two main differences between the NFC Forum Type 2 Tag platform and the NFC Fourm Type 4 Tag platform:
The Type 2 Tag platform uses "proprietary" commands on top of the framing protocol defined in ISO/IEC 14443-3 Type A. ("Proprietary" in the sense of the ISO standard which refers to such protocols as "Proprietary commands and protocols"/"PICC not compliant to IOS/IEC 14443-4". Of course the command set and protocol is well-defined from the point of the NFC Forum specifications.)
The Type 4 Tag platform uses a communication protocol based on APDU commands (ISO/IEC 7816-4 inter-industry commands) on top of the half-duplex block transmission protocol defined in ISO/IEC 14443-4. Type 4 tags can use either the Type A or the Type B framing/coding/activation protocols.
Type 2 tags have a flat linear memory structure (organized in blocks and sectors) which is also reflected in the commands defined for the Type 2 Tag platform: READ (a certain block of bytes within the current sector), WRITE (a certain block of bytes within the current sector), SECTOR SELECT (to select a specific sector).
The memory of Type 4 tags is organized in a file system. Consequently, there are commands to SELECT specific files (and applications), to READ BINARY data from these files, and to UPDATE BINARY data in these files.
That depends on the perspective.
From the perspecive of implementing low-level communication: no, the use different protocols and hence, access to the data on them needs to be implemented in (completely) different ways.
From a high-level perspective: yes, on top of both tag platforms (actually on top of all NFC Forum tag platforms) the NFC Data Exchange Format (NDEF) provides an abstraction of the actual storage technology. Hence, it's possible to provide application developers a means of interacting with tags independent from the actual tag technology. An API could (and does for instance on Android, Windows and other platforms) provide commands for reading and writing NDEF messages that work with any NFC Forum tag.