The naming scheme can be a little confusing. The ARK website helps clear up the features - http://ark.intel.com/
You can compare different CPUs to see the feature sets. The Core i3 tend to have smaller cache sizes and do not support Intel VT-d or AES instructions.
For labeling a CPU as "embedded" ... that is Intel's decision to extend a long life cycle to manufacturing for the component. Embedded means they have tested the part, see that is has a fit in the market segment and guarantee a minimum 5-7 year life cycle. ARK will also list which parts have an embedded purchasing option.
Thanks Brian for pitching in. Let me add a few additional comments:
First, you can find a lot more detail about the i3, i5, and i7 processors here:
Second, about the "embedded" classification. ... In addition to what Brian said, Intel supports its embedded customers in a different way from its PC OEMs. Intel has a special group dedicated to the embedded market and this group offers various programs such as training. development boards, tools loaner, system design assistance, to name only a few.... all of which is designed expressly to help embedded developers get their designs to market. These programs are focused exclusively to support the designated embedded parts.
I hope this helps.