In H 205, the digits refer to the size of the bearing it receives: sleeve 205 matches tapered bore bearings of that size, not a direct shaft dimension. The H series is the one for metric shafts. HA 209 and HE 213 belong to series intended for inch shafts: the bearing they mount may be the same as in the H series, but the sleeve bore is different.
In H 311 E, the final E distinguishes an execution of the same size, and other letters play that role too. Copy the complete designation of the removed sleeve. If what you have is the bearing designation, check that it ends in K: that letter indicates the tapered bore the sleeve needs.