Wood filler.

I’ve had luck using glue and sawdust from the wood being filled. Stain a piece of finish sanded scrap with the stain you plan to use. That will be your target. Then collect some sanding dust in a small container. Drip some stain in the pile of dust and mix it up. After it dries, compare it with the target board. Keep at it until you are satisfied with the match. Bear in mind that the dust will stain MUCH darker than the target, so be judicious in the amount of stain you drip into the dust.
Mix the matched, dried dust with some glue. Approach a school paste consistency. Rub the paste into the gap and allow to dry. Sand and stain the rest of the project.
Not a PERFECT solution, but tiny gaps will be far less noticeable.
Another solution I’ve used is application of Minwax filler and a Minwax stain pen. See it here. Click on the “COLOR” tab for a chart that will help match the pen to the stain you may use.
Best of luck.

-- Gene 'The true soldier fights not because he hates what is in front of him, but because he loves what is behind him.' G. K. Chesterton

I’m a big fan of Timber Mate. They have filler to match Many different woods. It is very easy to use dries quickly and sands easily. Woodcraft is my only source here.

-- " I'll try to be nicer, if you'll try to be smarter" gfadvm

I use Famo Wood. It comes in many colors and is readily available. If necessary colors can be mixed to get a shade you want.

-- Adversity doesn't build character...................it reveals it.

I’ve used Timbermate and Famo wood I like them both If at all possible i use real wood to fill gaps but if i can’t I use one of those two fillers

-- W James Brokenbourgh Custom furniture maker http://artisticwoodstudio.com/

PL’s woodpatch, takes stain well, and is easy to get from Lowe’s. It comes in oak, which is available there along with their natural, and smaller cans of various wood fillers.
The trouble with glue and sawdust is that it sometimes turns black, and is a pain to undo when it messes up.

-- The mark of a good carpenter is not how few mistakes he makes, but rather how well he fixes them.

I’ve been using famowood water based filler with good results but once I run out I’d like to try the timbermate. Both can have water added if they start to dry out.

-- He who dies with the most tools... dies with the emptiest wallet.