As mentioned in the comments פסיק רישא דלא ניחא ליה is probably equivalent to פסיק רישא דלא איכפת ליה. The Big Question is regular פסיק רישא vs. מלאכה שאינה צריכה לגופה
There is double machlokes that comes up between R.Shimon and R. Yehuda. R.Shimon holds "דבר שאינו מתכוון is muttar (Beitza 2:10), while R.Yehuda holds its assur. R. Shimon holds מלאכה שאינה צריכה לגופה is assur (rabbinically) while R.Yehuda holds it d'oraysa.
דבר שאינו מתכוון - when you do one act, and another secondary action also takes place. E.g. if you drag a light bench to bring somewhere, and it might cause a furrow to be dug, (the melahca of plowing). The shulchan aruch et.al. hold this is muttar (like R.Shimon), even if the secondary act is beneficial.
A פסיק רישא is a davar sh'eino miskavein where the secondary act is for sure going to happen. E.g. if you drag a heavy bench somewhere, and it will definitely cause a furrow to be dug (which is also beneficial). This is forbidden even according to R. Shimon, and many views hold it is assur d'oraysa.
A פסיק רישא דלא ניחא ליה is simply a פסיק רישא where the secondary act is not beneficial (or worse). For example, if you get no benefit from the furrow your bench creates. While there were some who permitted this, most hold it is rabbinically forbidden (see שו"ע או"ח סימן שכ:יח).
The standard case of מלאכה שא"צ לגופה is if you blow out a candle to make the room dark, but not to get ashes (the purpose of the melacha in the mishkan). I.e. you do a melacha but not לגופה, for its "purpose". The Shulchan aruch et.al. again hold like R.Shimon, though some (the Rambam) hold like R.Yehudah.
מלאכה שא"צ לגופה also comes up when you dig to get dirt, but it results in a hole being built (melacha of boneh). This leads to various complexities and there are many different interpretations on how it differs from פסיק רישא.
According to a standard explanation, when you do an action (digging) for a different purpose (getting dirt) we can show its in a different form than the melacha in the mishkan, but when you do a different action (dragging a bench), you're intent no longer matters, and it may be d'oraysa (of plowing). There are still some difficulties, so there are other explanations and divisions between d'oraysa and derabanan.