For Chess.com, that's the icons for a forced move. Or at least that's the file name, I haven't been able to find a central place for the icon scenarios.

Is it that “with attack” from the second image?

An attack is a great form of defense in itself and playing an aggressive, strong game from the beginning gives a player a significant advantage throughout the game.

With good enough counterplay, she might let you connect pawns. (Still reading the symbols, I don’t play chess :) )