Lathes and mills are the most basic machining tools and they both have lot of incommon even they may seen quite different devices.
Different chips from machining. When machining with high speeds or desired speeds ( according to the machne shop owner ), steel/iron would turn blue and high speed steel to grey. This pic also shows serpentine like chips which are really undesirable in machining as they tangle everywhere and don't remove heat as effectly from work piece than small chips.
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Tool bit condition:
If one wants a quality surface, the tool bit cutting edge has to be in good condition. Use your nail to feel if the cutting edge is uneven. Worst chipping you can see by naked eye. You can also use microscope to see the edge and it's condition.
Drill bit's cutting edge is sharp when the edge doesn't shine light == you can't see the edge.
Really unsharp drill bit.
Speeds ( and feeds ):
Speed rates as rule of thumb:
With carbide / hard metal tool bits (== those separate blade bits ): 30 000 / diameter ( of the work piece in lathe, and cutting tool in mill because those are the parts that actually rotate and define the cutting speed ).
With high speed steel ( HSS, drill bits are most common HSS bits ): 6 000 / diameter ( of the work piece in lathe and cutting tool in mill ).
With counter sink tools keep speed as low as possible, about 100 should be okay.
If your work piece in lathe is really thin ( like diameter of 6mm ), speed normally has to be lot lower than what the formula gives ( I used something around 1000 with one old lathe even formula would give 5 000 ). Also your machine defines a lot on what kind of speeds are realistic or even possible.