This information comes from the Tecplot Manual, pages 9-4 and 9-5.
Data and Styles are saved separately in Tecplot. The data is the plotted points, while the line style, view, and scaling of the plot are all part of the Style.
Your data only needs saved if you've changed it since loading it in. If you have, then you should go to /File/DataFiles/Write and choose either Ascii or Binary. Binary files are in a format readable only to Tecplot, but they load faster than text files. Ascii files are text files readable by you or another program. Text and geometries attached to the active window are also saved with the data. Datafiles should end with the extension ".plt"
The style of the plot is everything except for the data. You can save the file by going to /File/StyleSheets Write. A StyleSheet only covers the active Tecplot window. Style sheets end with the extension ".sty"
You can save the global colormap by going to /File/ColorMaps/Write. Colormap files include the colors used for contour flooding, Multi-coloring, and light-source shading.
You can save multi-window plots by saving a "Layout File." This saves everything about the current Tecplot session, including, the data, StyleSheet (1 per window), and Colormap. You can select this option by going to /File/Layout/Write. Layout files should end with the extension ".lay".