Understanding Learning Curves
I wouldn't interpret the first graph the same way. As far as know (and bear in mind that nobody knows everything), there's no clear way to distinguish between noisy features and bias (underfitting). But in either case there's no reason why the validation/CV loss would be much higher than the training loss, this is actually a clear sign of overfitting: if the model was not able to generalize, the training loss would be as high as the validation loss. Instead the model succeeds in representing some patterns, but it turns out that the patterns it captures don't apply (at least not as well) on the validation set. In other words, the model captures patterns which happen by chance in the training set: it overfits.
It's possible that adding more instances would help reduce the overfitting, as the CV loss appears to still decrease significantly in the 800-900 zone. But the difference is very large, so it's not sure that it can be solved only with more data.
I agree that the second graph shows some overfitting (as well), but not as much as the first one. In my opinion, the fact that the lowest difference between the two curves is not at the end of the curve points to either a model which is not stable yet (needs more data) or maybe there are simply not enough points on the curve to observe the real trend (i.e. the low difference at 240 and/or the higher one at 300 might happen by chance). This is indeed variance, but it's not very high
in my opinion.