Bubble shooter and clear-the-blocks puzzles, free
Games by Zaweba has both: Block Clear, where you pop groups of coloured blocks to empty the board, and Bubble Pop, an aim-and-fire bubble shooter.

Two games in Games by Zaweba answer this search. Block Clear is a puzzle where you click groups of touching coloured blocks to remove them and try to empty the whole board. Bubble Pop is a bubble shooter: you fire coloured bubbles into a cluster above and match three or more to burst them. Both are free, original and play offline.
They look alike at first, but they ask for quite different skills. Block Clear is slow and thoughtful. Bubble Pop is about aim, angles and keeping ahead of a ceiling that keeps coming down.
Block Clear: plan for the big groups
In Block Clear you click a group of two or more touching blocks of the same colour and it disappears. Blocks above drop down to fill the space, and empty columns close up to the left. The scoring is what makes it a puzzle: a group of n blocks scores n minus 2, squared. Two blocks score nothing at all, five score nine, and ten score sixty four. So the real game is waiting, and arranging the board so that one colour gathers into a big clump before you take it.
Clear every block and you earn a 1000 point bonus, which is often worth more than any single group. The game ends when no groups are left. Point at a group to see what it is worth before you commit, and press Z to undo the last move if a collapse goes the wrong way. Block Clear sits on the Puzzles shelf, and it is one of the best games in the app for a quiet ten minutes.
A good habit is to remove small groups of the colours you have least of first, letting the common colour fall together, then take that colour in one large group. Watch the left side too, since closed columns can bring far-apart blocks next to each other.
Bubble Pop: aim, bounce and burst
Bubble Pop is on the Retro arcade shelf, drawn in a 16-bit home computer style. You point with the mouse to aim and click to fire, or use Left and Right to aim and Space or Up to fire. Join three or more bubbles of the same colour and they pop, and anything left hanging with nothing holding it up falls away for bonus points.
The side walls are your friends. The aim guide shows how a shot will bounce, so you can reach a gap that has no straight line to it. Every few shots the ceiling drops a row, and if the bubbles cross the line the game is over, so there is always a gentle pressure to clear rather than tidy.
The biggest scores come from dropping, not popping. Pop a small group that is holding up a large hanging cluster and the whole lot falls. Look for those weak points before you fire.
Which one to choose
If you like to plan, start with Block Clear. If you like quick reactions and a bit of pressure, start with Bubble Pop. Both open on a title card with their rules and controls, F1 explains them during play, and Esc pauses. Your best score for each is kept on its tile in Games by Zaweba, on your own PC.
The app has 82 games in all, with no adverts and no accounts, so if one of these hooks you there is plenty more of the same spirit on the Puzzles and Retro arcade shelves.