The difference between a transmitter certified for use in SIL3 applications and a SIL2 certified unit is that the SIL3 unit will have satisfied more onerous requirements with respect to its design, in particular reliability and failure modes.
If you are talking about IEC61508/61511 SILs.
Note that the use of SIL certified devices, be they PLCs or transmitters etc. does not itself guarantee that you have satisfied the requirements for the safety function. It is the safety function itself (e.g. trip of plant item r items) which carrys the requirement for a specific integrity level. Therefore the whole of the system for that specific function (from sensor(s) to final element(s)) must be designed with the performance requirements and management requirments that come with the integrity level specified.
Use of certified devices does make the process of putting together your safety claims/arguments
easier and more traceable.
If you are unfamiliar with the design practices using the safety standards I suggest you get a specialist in who has a verifiable track record.
Hope this helps
A safety certified transmitter is different from regular transmitter as it has additional certification pertaining to IEC 61508.
It does not differ in operational functionality but has documented failure modes with identification of lambda, SFF and finally has a defined reliabilty.
You may achieve SIL3 risk miigation even by SIL2 transmitters used in 1oo2 or 2oo3 configuration as you meet the required Pfd(avg).
Even uncertified hardware can be used in SIL2/3 application if you can get safe and dangerous failure rates through OREDA or other reliability handbooks, achieve desired Pfd(avg) or compensate through enhanced loop inspection/maintenance frequency (though not desirable)as guided by IEC 61511.