The Telugu script, like the Kannada script, derived from the Old Kannada script. In fact, the demarcation between Kannada and Old Kannada is when Telugu and Kannada started to diverge. If there hadn’t been the Telugu branch, scholars would probably just talk about “Kannada”, and maybe talk about differences between earlier and later Kannada. Kannada and Telugu still look very similar.
Telugu has a very distinctive checkmark-shaped line at the top of many of its glyphs, in the places that most Indic scripts have a horizontal line (and Oriya has an arc).