BASE indicates baseband signaling - there is no modulated carrier, the frequency start near zero and extends to a certain cut-off frequency.
BROAD indicates broadband modulation - there is a wide frequency band with a number of carriers modulated with the data (similar to xDSL).
The X in -TX or -SX stands for 4b/5b (100 Mbit/s) or (improved) 8b/10b line code (PCS block code). The R in 10GBASE-SR or -LR stands for more efficient 64b/66b line code. A line code is required to enable clock recovery and bit-level synchronization. Without line code, the receiver would lose track of the bit boundaries when many equal bits are transmitted.
-T indicates a twisted-pair medium, two used pairs for 10/100 Mbit/s, four pairs for 1 Gbit/s upwards. Speeds beyond 100 Mbit/s use specialized line codes and scrambling.
-S stands for Short wavelength optical (~850 nm), -L for Long wavelength (~1300 nm), -E for Extra long wavelength (~1500 nm) and so on. With few exceptions, short wavelength is used with multi-mode fiber for short distance (less than 1 km), longer waves with single-mode fiber for long distance (1 km to 100 km). These three wavelengths are selected from the low-absorption bands of silica glass.
I've compiled a comprehensive and fairly complete list for Wikipedia a while back, all taken from IEEE 802.3.