It’s simple:

mBTC=millibitcoin=1 thousandth of a bitcoin=0.001BTC
uBTC=microbitcoin=1 millionth of a bitcoin=0.000001BTC

mBTC is equivalent to a Millibitcion which equates to 1 thousandth of a Bitcoin and numerically represented as 0.001BTC.
Similarly, uBTC is equivalent to a microbitcoin which equates to 1 millionth of a Bitcoin and numerically represented as 0.000001BTC.

Normal bitcoin is a unit of the commodity that can be traded.
Bitcoin has a cap of 21 Million bitcoins that can be released within the network.
There cannot and will not be more Bitcoins issued within the network once 21 Million Bitcoins are issued.
Bitcoin is made divisible to 8 decimal digits and beyond to infinity(on gaining majority vote through consensus) to encourage and sustain transactions post the 21 Million cap.

Here are some videos that do a great job of explaining how and why Bitcoin is divisible:

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