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What's the actual difference?

I've been told that they're the same thing; however, I seem to remember reading somewhere that where are different types of measures for field strength, denoted by the letters B and I think 2 others.

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It's the "old" way of speaking. If you are learning E&M now, most modern books will use SI units and the $\mathbf E, \mathbf B, \mathbf D, \mathbf H $ fields.

Nowadays, we call $\mathbf B$ the magnetic field and $\mathbf H $ just the "H field". In the older books, they call $\mathbf H $ the magnetic field, and $\mathbf B $ the magnetic flux density or something of that sort.

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