ACF fields work using standard WP functions for get_post_meta() and get_option(). The functions in ACF are only wrappers for these functions.
The problem is that if you use them on a field and you don’t use the ACF functions that the values will not be formatted for you.
For example, when you create an image field and set it to return a URL. ACF does not (and never has) stored the URL of the image in the field. ACF stores the attachment ID of the image. get_post_meta() is not a theme specific function, it is a WP core function and is always available.
In order to get the URL when using get_post_meta() you need to do the work of getting the URL field yourself.
$image_id = intval(get_post_meta('image_field'));
if ($image_id) {
$image = wp_get_attachment_image_src($image_id, 'medium');
if ($image) {
?><img src="<?php echo $image[0]; ?> /><?php
}
}
The same is true of any field that stores anything that is not a simple text value, like multi-select, page link, repeaters, relationship, post object, checkbox, taxonomy, flexible content, file, gallery, true/false, user, google map, date picker, time picker, and date/time picker fields.