How to interpret training and testing accuracy which are almost the same?
Why are the training and test accuracy almost identical?

Nearly identical performance on the training set and test set is a good outcome, it means the model is doing what it's supposed to do. To give an intuitive comparison:

The performance on the training set is equivalent to how well a student can redo the exercises which have been solved by the teacher during class. The student might just have memorized the answers by heart, so it's not a proof that they understand.
The performance on the test is equivalent to how well the student can solve some similar exercises that they haven't seen before in a test. This is a much better indication that the student truly understands the topic.


Does this mean that there is no overfitting?

Yes, it proves that there's no overfitting. To keep with my comparison, overfitting is equivalent to memorizing the answers.
However there can be other problems which bias the result:

The performance on the test set is 2 points higher than the performance on the test set. This probably means that the test is very small, because if it was a large enough sample the performance wouldn't be higher. If the test set is too small, the performance is less reliable (any statistics obtained on a small sample is less reliable).
Accuracy can be a misleading evaluation measure. It only counts the proportion of correct predictions, so if a large proportion of instances belong to the same class then the classifier can just predict any instance as this class and obtain high accuracy. For example here if the majority class is around 63-65%, then it's possible that the classifier didn't learn anything at all. Looking at precision/recall/F1-score gives a more accurate picture of what happens.

[edit] Important note: as Nikos explained in a comment below, my answer assumes that you have a proper test set, i.e. that the train and test sets are sufficiently distinct from each other (otherwise there could be data leakage and the test set performance would be meaningless).