細い and 薄い: thin lines and thin layers
Distinguish slenderness from thickness using lines, string, and paper, and identify other senses of 薄い.
The slenderness of lines and string
細い糸で縫いました。 says that someone sewed with fine thread. 細い, read ほそい, describes the small diameter or width of something long.
細い線を一本引いてください。 asks someone to draw one thin line. It concerns the line's width, not necessarily a pale color.
The thickness of sheets and boards
この紙は薄いので、裏の文字が見えます。 says that the paper is thin, so the writing on the back shows through. 薄い, read うすい, describes a small thickness between two surfaces.
薄い板を細く切りました。 says that someone cut a thin board into narrow strips. 薄い describes its thickness, while 細く describes the narrow cut.
Separate line width from color
この線は細いですが、色は濃いです。 says that the line is thin but dark in color. Width and color intensity are separate properties.
線が薄くて読みにくいです。 can mean that the lines are faint and hard to read. Unlike thin paper, 薄い here concerns the strength of a visible mark.
Must a 細い線 also be pale?
Show the answer and why
No. 細い concerns width. A line can be narrow and dark; 薄い can describe its color being faint.