Disambiguating eval, obj (objective), and metric in LightGBM

I'm asking this in reference to the R library lightgbm but I think it applies equally to the Python and Multiverso versions.

There are 3 parameters wherein you can choose statistics of interest for your model - metric, eval, and obj. I'm trying to clearly distinguish the different roles of these 3 in plain language.

The documentation says:

obj objective function, can be character or custom objective function. Examples include regression, regression_l1, huber, binary, lambdarank, multiclass, multiclass

eval evaluation function, can be (list of) character or custom eval function

metric had no R documentation, except for the catch all that says "see paraters.md", which also doesn't really explain it, but which lists the following options:

metric, default={l2 for regression}, {binary_logloss for binary classification},{ndcg for lambdarank}, type=multi-enum, options=l1,l2,ndcg,auc,binary_logloss,binary_error... l1, absolute loss, alias=mean_absolute_error, mae l2, square loss, alias=mean_squared_error, mse l2_root, root square loss, alias=root_mean_squared_error, rmse huber, Huber loss fair, Fair loss poisson, Poisson regression ndcg, NDCG map, MAP auc, AUC binary_logloss, log loss binary_error. For one sample 0 for correct classification, 1 for error classification. multi_logloss, log loss for mulit-class classification multi_error. error rate for mulit-class classification Support multi metrics, separate by , metric_freq, default=1, type=int frequency for metric output is_training_metric, default=false, type=bool set this to true if need to output metric result of training ndcg_at, default=1,2,3,4,5, type=multi-int, alias=ndcg_eval_at,eval_at NDCG evaluation position, separate by ,

My best guess is that

1. obj is the objective function of the algorithm, i.e. what it's trying to maximize or minimize, e.g. "regression" means it's minimizing squared residuals
2. eval I'm guessing is just one or more additional statistics you'd like to see computed as your algorithm is being fit.
3. metric I have no clue how this is used differently than obj and eval