Technically, pilates is not strength training. It may serve to improve your muscle tone but I doubt after even extensive use of pilates you could lift much more weight. In very non-technical terms strength training involves exhausting the muscle very quickly by applying resistence. Strength training is progressive. Once you can handle a certain amount of weight, you increase the weight. As you body adapts, you increase the weight more. The largest increase in strength will occur when you work anaerobically. In weight training terms, strength training is very often low rep, high weight routines. Body building by contrast is mid-rep moderate weight. Toning is light weight, high rep. I would put Pilates in that category.
Having said all that, I think the jury is still out with regards to the health benefits specifically attributed to strength training as opposed to other forms of exercise. Certainly it has it place in sports improvement, mobility and performance. In my opinion, if you don't like the idea of strength training and you don't need it for any kind of mobility improvement, rehabilitation then do the exercise you can stick with. There's no benefit in taking up a training regimen that you hate to do.