Most toothpastes contain a polishing agent that is often diatomaceous earth or other forms of fine ground silica which helps to scrub away surface stains on teeth. This is a cleaning action not to be confused with “whitening” which implies a bleaching action producing a tooth colour intrinsically lighter than before. For this to happen there needs to be a bleaching agent present in the toothpaste of sufficient strength to bleach tooth substance. Critically also the toothpaste needs to be on the teeth long enough for the bleaching agent to work.
So you can probably see the problems here with so-called “whitening” toothpastes. First the bleaching or whitening agent has to be totally safe. This means that commonly either sodium bicarbonate or sodium perborate are used, neither of which is especially good at bleaching, especially in the low concentrations that have to be used in toothpastes in order to conform to health and safety regulations. Then there is the problem that the toothpaste does not stay in the mouth very long, 3-5 minutes probably at most, and often for much less time. It seems highly unlikely therefore that any toothpastes will significantly whiten your teeth, although some are better than others at keeping them clean. Be sure though, that your “stain removing” toothpaste is not too abrasive since this can wear away the enamel, especially if an inappropriate technique is used (like too much horizontal brushing across the face of the teeth), and cause sensitivity of the teeth in time.
Thus most so-called “whitening” toothpastes are formulations that are somewhat more abrasive than the average toothpaste and are therefore more effective at removing stains on the surface of the teeth, rather than being able to whiten teeth in the true sense of the meaning. The latest types of whitening toothpastes incorporate generous amounts of calcium and phosphate in in order to help repair surface damage on tooth enamel caused by abrasion, and therefore produce a smoother enamel surface which reflects light better and therefore makes the teeth look shinier. Again this is hardly true teeth “whitening”.
Thus a “whitening” toothpaste is unlikely to make your teeth actually whiter or lighter in colour than they naturally are, but it is useful to use one with an up to date formulation for your daily brushing since it is likely to give the best all round results. Some contain anti-bacterials or chemicals designed to prevent plaque from easily adhering to the teeth, and these may be helpful, as too can be a small amount of fluoride to strengthen the enamel against tooth decay. Use a good toothpaste by all means, but don’t expect miracles from it, and you should appreciate too that the mechanical removal of plaque from your teeth by correct brushing technique is much more important in keeping your teeth looking nice than the actual brand of toothpaste used.