General object recognition with biggest number of classes
First, to level set on terminology.
Image Classification based neural networks, such as Inception and Resnet, classify an entire image based upon the classes the network was trained on.  So if the image has a dog, then the classifier will most likely return the class dog with a higher confidence score as compared to the other classes the network was trained on.  To train a network such as this, it's simple enough to group the same class images (all images with a dog) into folders as inputs.  ImageNet and Pascal VOC are examples of public labeled datasets for Image Classification.
Object Detection based neural networks on the other hand, such as SSD and Yolo, will return a set of coordinates that indicate a bounding box and confident score for each class (object) that is detected based upon what the network was trained with.  To train a network such as this, each object in an image much as annotated with a set of coordinates that correspond to the bounding boxes of the class (object).  The COCO dataset, for example, is an annotated dataset of 80 classes (objects) with coordinates corresponding to the bounding box around each object.  Another popular dataset is Object365 that contains 365 classes.
Another important type of neural network that the COCO dataset provides annotations for is Instance Segmentation models, such as Mask RCNN.  These models provide pixel-level classification and are extremely compute-intensive, but critical for use cases such as self-driving cars.  If you search for Detectron2 tutorials, you will find several great learning examples of training a Mask RCNN network on the COCO dataset.
So, to answer your question, Yes, you can use the COCO dataset (amongst many other options available publicly on the web) for object detection, or, you can also create your own dataset with a little effort by annotating your own dataset with bounding boxes around the object classes you want to train.  Try Googling - 'using coco to train ssd model' to get some easy-to-follow tutorials.    SSD stands for single-shot detector and is an alternative neural network architecture to Yolo.
I'm new to the computer vision world, I'm trying to create a script with the objective to gather data from a dataset of images.
I'm interested in what kind of objects are in those images and getting a summary of them in a json file for every image.
I've checked out some YOLO implementations but the ones I've seen are almost always based on COCO and have 80 classes or have a custom dataset.
I've seen that there are algorithms like InceptionV3 etc. which are capable of classifying 1000 classes. But per my understanding object classification is different from object recognition.
Is there a way to use those big dataset classification algos for object detection?
Or any other suggestion?