When you're saying 'isoelectronic' you're using molecular orbital theory (bonding pairs, non-bonding pairs and anti-bonding pairs), which is distinct from valence bond theory (single, double bonds, lone pairs). In molecular orbital theory, concepts such as 'double bonds' and 'lone pairs' are not so important. By saying that B-N bonds are isoelectronic with C-C bonds, you're saying that the energy diagrams for the two, filling from the bottom orbitals to the top, are the same. In valence bond theory, B-N and C-C are clearly different (dipoles, lone pair on the nitrogen, etc).
Molecular orbital theory and valence bond theory both have their advantages and disadvantages so chemists tend to use whichever one is easier for what they're doing at the time. However, these two theories are different concepts and this is often poorly taught to students. For example, things get very confusing when a lecturer suddenly switches from using the double bonds of VBT to the energy diagram of MOT to explain aromaticity.