Does recall has different interpretation when comes to classification and information retrieval

Recall Definition

In terms of classification

The recall is defined as no of positive instances that are correctly detected by the classifier.

$$TP = \frac{TP}{(TP+FN)}$$

In terms of Information retrieval

Recall is defined as No of relevant documents that are retrieved.

 Let p = No of relevant documents that are retrieved   and
q = Total number of relevant documents

Formula  = p/q


Do both the definition work on any common understanding?. I still can't get my head through this. If both are different, why are they using the same name recall?

According to wikipedia, Recall is defined as-

In information retrieval, recall is the fraction of the relevant documents that are successfully retrieved.

In your second formula, recall = p/q, where q is total number of relevant documents. If you define a confusion matrix for binary classification, you will see that q is actually sum of TP and FN. And p is already (by definition) is TP.

Now lets get the definition of TP and FN. TP (True Positive) is number of predicted positive docs out of number of actual positive docs. FN (False Negative) is number of predicted negative docs out of number of actual positive docs. So, basically when you add TP and FN, it becomes total number of positive docs.

So, let say out of 50 positive (actual) docs, you get 35 positive and 15 negative predictions. So, recall by your first formula is

$35/(35+15) = 35/50$

and by your second formula, $p = 35$ and $q = 50$, so recall is

$p/q = 35/50$

Hope this helps. Please comment if I am wrong about something or missed anything.